The Genoese Emporer

[unmerged(6159)]

Chas, great to get the feedback. I'd like to believe that someone else is thinking about this, and you clearly are!

I understand your point, but it can't be a province weighting issue. I belive what my test show is that the countries I'm calling 'voters' have votes that count at least as much as HAB. Those I'm calling non-voters have votes that count at most about 1/4 of HAB. Obviously my big assumption here is that HAB self relations is not treated in a fundamentally different way that HAB relations with other countries. This can be tested but will take some time (i.e., a lot of tests). And your criticism is exactly what I deserve for giving out my test results in dribbles as I complete them.

My next test were - Baden, reducing HAB-BAD from high test 0/5 elections for HAB, increasing from low 5/5 for HAB. Baden is a voter. WUR HOL and SAV all give the opposite, the reduction from the high gives 5/5 for HAB the increase from the low 5/5 for HAB. None of them votes.

So relations summary of the voters as I understand it right now:

		GEN		HAB
Voters
KOL		200		105
BAY		200		73
HES		200		4
PRU		-199		4
KLE		200		4
BAD		200		57
HAB		200		46/61
Probable Voters
HAN		71		15
Ambiguous
PFA		-100		15
sum		972		305/320
Proabable non-voters
BRA		-112		12
SAC		4		11
Non-voters	
HSA		-96		-5
THU		158		53
WUR		166		1

I've ignored SAV and HOL who I know don't vote.

So there is no obvious reason why 972-320 is a win for HAB and 972-305 a win for GEN.

My next step is to look into the unclear results some more, and work on switching the HAB tag. However, any advice or hypothesis I can test would be appreciated.

On mouseovers, the mouseover is set by the member HRE bit or whatever the real name is. The mouseovers in the IGC are different from the original mouseovers. So there is no doubt in my mind that the mouseovers are indeed stored seperately from the algorithm that actually chooses the emperor

 

[unmerged(6159)]

I can't make the table format work. Any help?

 

[Chas]

I have been playing around with some Knights saves. I also am being very rigorous and careful, so try to believe at least the facts of what I say below.

1) Electors

I'm not being deliberately argumentative (you know I would not be even looking at this if I wasn't impressed with your game and research) but I'm still not convinced about your argument re the mouseover electors. OK, so you know (which I didn't) that there is a bit somewhere that can be set and is different in the IGC. But why shouldn't this bit be used for the election?

Anyway, I am ABSOLUTELY CERTAIN that BRA is an elector, see below.

I didn't fully understand your distinction between non-voters and non-electors, so maybe you agree with this anyway. If not, you MUST look at section 6 below.

Do you mean that BRA, say, is an elector, but may not vote depending on specific circumstances (e.g. hypothetically vassal electors don't vote, or vote the same way as their owner, or whatever)

2) Elector rels vs Candidate rels

One thing that intrigued me is whether the program goes through the candidates checking the elector rels (and anything else it might do) or whether it runs through the electors, checking the candidate rels.

As you of course appreciate, each rel appears in the save file twice.

Cynical as I am, I expected programming errors to have introduced inconsistencies so that, for example, FRA-SPA rels might be +190.000000 and SPA-FRA rels might be +189.566131. I have checked a lot, and have found no inconsistencies anywhere.

By altering only one of the pair of rels, it is easy to check which way the program is doing things. In fact, the program runs through candidates (presumably all catholic countries) checking rels. So it does not matter what e.g. the BRA-HAB rel is, only what the HAB-BRA rel is.

In my testing, I am only altering candidate rels.

What are you doing? I don't mean to be insulting, but if you are changing only one of the rels, and the wrong one, it would explain why sometimes you are finding that certain countries appear not to vote, e.g. BRA

3) Test procedure

1 exit the game
2 alter things in wordpad
3 load the game
4 load the save
5 run for 5 days, up to the election
6 reload the save
and repeat 5 and 6 until satisfied

So I do not exit the game between each test. Do you? I am assuming that the random number generation system in EU means that it does not matter. I am encouraged to think this by:
- I do get different random results from the same save file (once circumstances are right, of course)
- We do get a different hint on each reload, so something is obviously different each time

The reason I exit the game to use wordpad is that the save file is locked if I do not, so that I can't just ALT-TAB and alter things. It is even locked if I reload from a different save file!! I am very surprised at this - it seems that any file that has been used at all during a session is locked until the end of the session, very quaint.

Are you doing the same?

4) The game proper

I was not completely consistent during the game proper. I fed every bit of money I had into rels with mouseover electors. After I got to +200 with all of them (around the 1680's):
- Occasionally one of the electors would offer me an alliance, which I mostly turned down - then I would restore from +190 to +200 with whoever it was shortly after - typically 1 - 5 months later.
- Sometimes I would accept the alliance from boredom (I always dishonoured so I had no wars at all in the 300 years).
- BOH was a vassal of BRA, so I had no RM, so my rels would progressively dip a little from +200. Generally I topped up with a letter once they got down to +197, sometimes +198
-This means that I am not absolutely certain of the precise position on alliances and rels in May 1705, which is when my test election takes place. I do know that BRA was at +200. I'm not sure if I had an alliance at the time. I'm not sure where the BOH rel was, between +197 and +200
- I did not save when I lost that election in the game proper (else I would know these things). But I definitely DID LOSE THAT ELECTION. This is verified by my subsequent save. And I am ABSOLUTELY CERTAIN that once I won an election, I never lost one
-My prior save was in 1695

4) The Base case
-I took the 1695 save and ran forward, declining alliances, and restoring rels with letters and gifts. I saved on 1st May 1705. This is my base case.
- The Austrian emperor dies on 5th May 1705, so my tests are to load a game and run for 5 days. There is a tiny bit of random variation in what happens in the game during those 5 days (e.g. sometimes France settles a peace with BRA during that period, sometimes it doesn't), but nothing that affects my rels or HAB rels
- There are only 7 mouseover electors left in the game. Rels in the order HAB/KNI are:
HAB 20.3 200.0
PRU -8.0 200.0
BAY 200.0 200.0
BOH 14.9 199.9
PFA 61.1 200.0
SAC 56.0 200.0
BRA -138.3 200.0

TOTAL 206.0 1399.9

These figures are rounded to the first decimal place from the save file values, using normal 4/5 rounding rules

5) Base case results
KNI always wins!! (12 tests)
This is why I've gone into detail above about how I ran things during the game - I lost in the game but now always win. This is one of the things that really puzzles me, after all, I'm being honest about my level of certainty in the game situation, but anybody would agree that they are virtually identical.

See the demoralising section 12 below.

6) KNI-BRA 180
I alter (in the BRA section of the save file, see section 2 above) the KNI rel from +200.0 to +180.0
Now HAB sometimes wins (4 out of 12 tests), KNI wins the majority, nobody else ever wins

7) KNI-BRA -200
HAB always wins - 6 tests

8) KNI-BRA 0
HAB always wins - 6 tests

I have done a few single tests at intermediate values, they are consistent with tests 5,6,7 and 8.
As far as I am concerned, sections 5,6,7 and 8 mean that BRA IS DEFINITELY AN ELECTOR. Progressibe worsenign of the BRA-KNI rel changes the result from KNI always wins, through KNI sometimes wins, to HAB always wins.

9) Get France to win
FRA has rels of between -0.2 and 39.6 with the 7 mouseover electors. This puts it 3rd on a simple total of rels, behind KNI and HAB (I have constructed a matrix with all catholic countries and all mouseover electors, so I can be sure of this)

I alter FRA rels with all 7 electors to +200 (leaving KNI and HAB alone). This means that FRA has slightly better total rels than KNI, because KNI-BOH is 'only' +199.9

FRA wins 16 out of 23 tests. KNI wins the others. HAB never wins.

10) As 9, but with BRA-KNI from +200 to +180
So this is sort of a combination of section 6 and section 9.
Now FRA wins 17 out of 20, HAB WINS THE OTHER 3, KNI NEVER WINS

Now I'd forgive you if this seems a bit hard, but as far as I am concerned I am pretty much 100% certain now that the election is some sort of a run-off between 2, and only 2, candidates. I have no idea how it works, but one of section 9 and 10 are the best possible chance of getting 3 different winners appearing in the result, and it never happens.

Section 9 also means that the run-off is NOT between the current incumbent and the best other candidate (which I thought was a possibility until conducting the tests)

11) Weightings/ bonuses
You seem sceptical about weightings, but surely there simply must be something:
We know that rels have something to do with the result, becasue altering them can change the result.
We know that a country like KNI can lose even when its rels, any way you care to assess them, are vastly better than the country that actually wins the election.

Possible factors/ weightings etc. to consider
- The 'bigger or stronger' the elector, the more his votes count (any of the many possible measures of size, see below)
- the 'bigger or stronger' the candidate, the more his rels are factored up (any measure of size)
- the incumbent gets a bonus, depends on the election system how, could be lots of different ways
- The religious tolerance settings of the candidate affect the votes (e.g. BRA-FRA rel of +200 counts for more if FRA is tolerant of Protestants than if not etc). I have run some tests on this case and can find no conclusive effect, though it needs a lot of tests to be sure there isn't some small effect.
- The more diplomatic VP's a candidate has, the more his rels count (you can see the sort of rationale that might apply)
- The more total VP's a candidate has, etc. etc.
- The stronger a candidate monarchs diplo rating the more his rels count
- The stronger an electors monarchs diplo rating, the more his rels count. This is a little harder to believe, but again, you can see the sort of rationale that would be used: "Bohemia's monarch is very influential, so which way he votes affects the result more strongly" etc.
-Both the above for the total of all 3 monarch factors. Possible rationale "we want a good administrator and strong military leader for an emperor, not just a good diplomat" or "Bohemia is only more influential if its monarch is adminstratively and militarily strong as well as diplomatically strong"

In all the above, weightings can easily be replaced by bonuses e.g. You get +500 electoral points for being the 'bigger' of the 2 candidates. The possibilities are almost limitless.

'Bigger/stronger' could be based on:
- No. provinces
- No. of cities
- No. fortified cities
- Total census tax income last year
- Total wealth last year
- Total manpower
- Total population
I can't see the programmers doing anything too complicated.

Do yu have any instincts? I still think that it would be consistent with the style of the game for candidate monarch diplo values to have an effect.

The game designers may have wanted to stop countries like KNI from artificially winning the game with relatively modest rels, or by ensuring that KNI is just 1 rel better than HAB, for all electors. So they may well have come up with something that weights in favour of candidate size, strength etc.

They may have wanted to ensure that HAB often won (the game does seem to have some features designed to generate some kind of spurious historicity). Bib seemed to hint so in his outrageous post in this thread - but I am not convinced by much that Bib says, and he does love to cause a bit of mischief. Section 9 above suggests to me that it isn't like this (HAB is the incumbent, it's rels are unchanged, KNI's rels are unchanged, but it's always one of FRA and KNI that wins).

12) Unsaved factors
This is a horrible one, that is very corrosive of confidence in doing tests. We know that not everything that should be in the save file is there, e.g. random event effects.

What if there is some factor that is lost on a reload? e.g. some moving average of rels that ensures that KNI can't for example, spend a fortune in the 24 months before an election, zoom up the rels and pinch the emperorship. I would be absolutely certain that this is the case from my own game, if only there was not that smidgin of doubt over my BRA alliance and the exact BOH rels that I discussed in section 4. I guess this is obvious - if I lost in the game, but win every time on the re-load, it proves that there is an unsaved factor - but only if the circumstances in the game on May 1st 1705 were the same as my current base case - they nearly were, but maybe not exactly.

The problem with this is that one would have to conduct tests starting anywhere up to 50 years before an election, and I don't have the energy to even try this.

I will pm you my e-mail address to avoid cluttering up the thread further.

 

[unmerged(6159)]

Great post! Fantastic to have some support on this.

Let me go through a few of your points
1) This is largely semantics. I'm calling voters or electors countries that BY MY TESTS have been shown to affect the outcome of the election. I agree that I haven't yet proven much, but my results must be consistent with the real answer.
So your tests (which are almost identical to mine) show that BRA makes a difference. However, I notice that with a change in rels of 20 they still hadn't made much difference and I've seen multiple countries reverse the election with a swing of 15. So my calling BRA a non-voter is a short way of saying that it failed my test of who swings the election totally the other way based on 10 tests and a 15 swing in relations.
2)I've been switching both relations (i.e. BRA-HAB and HAB-BRA). I figured the consistency might be necessary, or that the program may symmetrize the matrix in some way. So I don't think this explains my results.
3) I've been doing exactly what you've done except that I generally go through 4-6 files while I'm in wordpad. It is just too time consuming for me to exit each time. I have done multiple tests at intermediate values, and the trend looks decent. I haven't done any statistical test to see if the randomness is good, but I think there are bigger fish to fry.
4) I did a similar thing with an election I lost. I played from my original save in 1612 and just added relations through 1619, and saved at that point. From there I adjusted HAB slef relations to find the relations where the election flips.
11) I'm only sceptical about weightings because 1) they are so hard to test 2) I'd prefer to think that a simpler solution has been implemented. The fact that you see very little change based on a 20 poitn swing for BRA certainly suggests that they have some sort of negative weighting. Note however that my testing has found 6 countries (in my save) whose weight is at least as big as HAB, (unless self relations are treated differently than others) so I have doubts about 'bigger stronger' type weightings on the elector side. Also I suspect self-relations were left in there by accident so they ought ot be the same as all others, if not a lot of my assumptions are likely wrong.

Very interesting about the run-offs. I agree that your tests should have shown up 3 different winners. My suggestion is 1) the code determines the 2 'best candidates and then 2) it adds a random factor which is 0-15 in my case to determine the winner.

I'll still plan to test DIP ratings next, and expand my numbers on the incumbancy bonus (which by my tests is a small factor). I'll work on BRA too, but our results are consistent.

As to cluttering the thread - yeah it'd be good to do some of the back on forth off line, but anybody who makes it through the AAR can stop at the end, and I'd like to keep some of this public so that others can add suggestions.

 

[unmerged(6909)]

Sorry for disturbing you, but I have just read this AAR and think it's good stuff. Well, my additions are a bit out-dated....

Becoming HRE:
Sorry, no real knowledge here. I hope that you'll find the key. Good stuff so far.

12% provinces:
Isle Royale
Kitimat
the Aleutes island
the southern most island of South America (not the falklands iirc)
Macquerie
The southern island of New Zealand

CoT
Yes, high trade tech is one of the keys, though you have to be in the latin or orthodox tech group. With Russia, England, Holland,... no problem. Turkey, The Mughals: I never got a single CoT even when I had trade tech 10 compared to 5 (any other major) and a lot of TP's around the same colonies. Then a european power comes by, places a level 1 colony somewhere et voila... they get a CoT.
So having TP's around is helpful but not neccessary. More important is the existance of trade generated which belongs to a muslim or pagan controlled CoT or a european CoT far away.
There are some traditional places for CoT in Asia:
Khreset/Nagorje: The best choice for a CoT if you want to keep it secret. Place a TP at the coast and unlike RoTW you can build a colony in any adjacent province. It's hidden then from any explorer sailing along the coast and stays secret if you cover the sourrounding provinces.
Timor, Samar, Mindoro, Taiwan, Jakarta: Each of them has some dis(advantages). Jakarta is cheap with high chances of succes, can get the trade from India and China. Taiwan is the closest province to China, so you'll keep the chinese trade no matter how many CoT pop up in the future but it's known to China and Japan iirc. Low chances of success.
MacQuirie is also very likely to get a Cot, Tahiti, Hawaii, Kitimat/the Aleutan island, too.
You can find the chances for each province to become a CoT somewhere in the FAQ or on private pages. It's different for each province. I prefer to colonize mainland provinces to get a CoT there to use the additional growth for neighbouring provinces and place TP in other provinces. Monterrey is an example. Kitimat will become a colony afterwards.

Competing in CoT:
You asked why nearly noone wants to send merchants to Tschumkan. The distance to your capital plays a (minor) role, too. I don't know how distance is calculated in EU.

Diploannexing:
You tried to vassalize Cologne. They had relations of 200 with Genua and Austria. This prevents vassalization afaik (I've read it somewhere in this forum, I also tested it from time to time in my own game. Seems to be true so far. This doesn't prevent them from dying without an heir, of course. Maybe a good idea to prevent other nations from getting diploannexed by keeping tzhe realtions with them at 200).

 

[Lord Durham]

Issac B: Is this what you're looking for?

     KOL    200      105
     BAY    200       73
     HES    200        4
     PRU   -199        4

Use the "quote" button to see how it works if this is it.

LD

 

[Chas]

Erratum: on re-reading my long post, I see that I have been more rigorous about testing than writing posts! For the avoidance of doubt, it is candidate rels that matter, and it is candidate rels that I have been altering, despite the fact that in section 6 I say that I am altering an elector rel - that was just a mistake in my write-up.

Non-electors: OK, so it represents what you have found on a 15 point swing. I think you may find it a long job going at it this way though - I am preferring to find swings that affect things, at least that way we start to build up a picture of what matters. As you are well aware, the 15 point swing only arises because that is what is necessary for your HAB self-rels to affect things. I assume (yes, possibly wrongly) that different swings will affect things for different candidates.

Special effect of self-rels: No, I'm not saying that I think they are special, and whilst it's very rigorous of you to leave the option open, I wouldn't worry too much about it. And I'm afraid I doubt very much if self-rels were left in for a reason. Think of it from a programmers point of view. Much the easiest way of handling the rels is:
-every time a country dies or is born, you update a single list of countries
- every time a rel affecting event takes place you run down that list updating the rels, for every affected country - much easier if you don't have to check whether this is a self-rel
- To display the rels for each country you just display the single list, not a special list for each country

So far as I can tell, self-rels do vary in the same way as ordinary ones i.e. they are never very good ('cos you can't send letters to yourself). Goody-goody countries tend to hover around the 0 to + 10 area. Countries that do nothing (e.g. my KNI) stay at 0. Bad boys self-rels progressively deteriorate to -200.

I've seen posts in earlier HRE threads that suggest that self-rels are a feature not a fault, but I wasn't convinced - they were mostly from the establishment, who after all are paid to convince us that what Paradox don't have the budget to alter is alright really.

Hmmm, interesting that you think that the 20 swing in BRA-KNI rels hadn't made much difference. My view was that, given that KNI is miles ahead of HAB, it is astonishing how much difference a 20 point swing on one country makes. And leads me to tentatively suspect that there is some massive multiplier/bonus being applied to bigger/stronger candidates. I will find out how big a swing totally reverses the result and let you know. From single tests I think it may be around 40-50 (so I can be +200 with all mouseover electors except one where I'm +150ish, and still lose the election, even though HAB has very modest rels, and is worse on every country, including the one that I'm +150 on)

Your test: I've looked back at your original game posts, but just confirm for me whether your position is the same as mine: an election that you lost in the game, you win every time on reload (for the base unmodified case), and you believe the save file is pretty much the same as the situation in the game. 'Cos this is quite a big deal really. We may be condemned to discovering, at best, the way the election works on re-load and still be left in the dark about unsaved factors. And you just know that the establishment will throw every obfuscation possible at you if your proposed answer isn't 100% replicable in game play - they don't want you to find the answer, they want it to stay a mystery.

Run-offs: Yes, I also suspect that it determines the 2 best candidates, and that there are random additions.

I think it would be consistent with the way some other parts of the game are handled if the random addition is related to a factor e.g. add a random number between 0 and the candidates monarch diplo rating, perhaps multiplied up by some constant to get the right monarch-diplo effect.

In fact, I checked if your HAB monarch diplo rating was a factor of 15 but it doesn't seem to be. The problem is that the sum-of-rels might be factored down (e.g. divide by 10 and truncate any decimal places) before applying a random addition, so it's going to take a lot of testing to fathom the answer, and it seems to me it's a lost cause unless we have a definitive list of what factors (in the save file at least) can affect the result.

I also tend to favour candidate factors being more likely than elector factors - too much hard work for the programmers to do electors.

Weightings: But how on earth does HAB ever win in your case or mine, if there isn't some weighting/bonus/something. Yes, 15 points swings your election, but that's in a situation where on sum-of-rels HAB shouldn't get a look in at all.

 

[unmerged(6159)]

I think you're being a little conspiratorial, but I agree that the only help we get is from neutral users like oursleves. I note that the FAQ is without a doubt wrong, and hasn't been unstickied or had any notice from moids. [mods - prove the conspiracy theorists wrong]. My save game is not the same as the in game one. I had to play from 1612 and I spent a lot more on gifts than the original time around. And Genoa didn't win by much from the second save I only had to increase HAB self relations by 30 or so to see them start to win some elections.

The idea of a multiplier for bigger/stronger candidates is certainly plausible. Tricky to test. For the moment I'd like to understand my weird results for BRA and PFA.

For Brandenburg I increased the swing to 30 relationship points. This still wasn't enough to totally change the outcome. From the 'HAB always wins' save, a reduction in BRA-HAB by 30 points gave Genoa 8/10 elections. From the 'GEN always wins' save an increase in BRA-HAB by 30 gives HAB 6/10. I ran further tests with the change of 15 also so my results are

HAB self    BRA HAB   GEN wins  HAB wins
61___________12.2________0_________25
61___________-2.8________2__________8
61__________-17.8________8__________2
46___________12.2_______25__________0
46___________27.2________7__________3
46___________42.2________4__________6

So yes BRA counts, but less than most electors.

I think I will next map out the number for BRA to see how it compares to 15 which is the number for HAB-HAB relations. I'll then try to compare it with the effect of BRA-GEN which should give some insight into weighting factors.

I've done 5 more tests of the same save with SPA and GEN as incumbents. Results

Incumbent    HAB wins   GEN wins
HAB____________25__________0
SPA_____________7__________3
GEN_____________8__________2

which I can't say I understand. Maybe I'll run more tests here.

I also went from my 'HAB always wins' save and changed the Genoese DIP from 4 to 8 in the save. HAB won 10/10. I then went from my 'GEN always wins' save and changed GEN DIP from 4 to 1. GEN won 10/10. I haven't tried with HAB DIP values as it's the HAB king who dies for my election. But it looks like DIP isn't the answer.

 

[Chas]

Lots to report, not all of it good.

1) In my KNI-always-wins base case, he doesn't
I got a spurious result, so I did a lot more (72) tests of my base case.
Results:
KNI 62
HAB 10
Conclusions:
- There's something seriously wrong with my head doing 70+ tests
- I'm now very wary of any 'always wins' conclusions
- So my loss in the game may just have been my dumb luck, and there may be no unsaved factors - which would be nice.

Anyway, KNI wins enough that I can identify swings with certainty

2) You can get 3 winners, it isn't a 2 horse race
Because of the above, I went back and did a lot of tests (64) on a designed case
The case was:
FRA = +200 with all 7 mouseover electors
KNI = +200 with 5, +199 with BRA, +199.896667 with BOF
HAB = as base case, a mix of rels between -138 and +60 with BAY at +200
Don't ask me to rationalise the KNI design, it meant something at the time but now I'm not convinced
Anyway, results:
HAB 5
KNI 26
FRA 33
Conclusions:
- Yes, my head is in serious trouble
- You can get 3 winners. Sorry about yesterday's red herring

3) Electors
As promised I tested my base case with KNI-BRA at +150 (instead of +200)
I then tested the other mouseover electors, each time reducing their rel to +150
The 50 reduction in rels is not as scientifically devised as yours, just enough to demonstrate that a relatively small reduction on one elector swings the result.
Results:
Elector, Tests, result
HAB, 5, all HAB
PRU, 5, all HAB
BOH, 5, all HAB
BAY, 5, all HAB
PFA, 5, all HAB
SAC, 5, all HAB
BRA, 10, all HAB

Would I have got some KNI results if I'd done 70 tests on each? Dunno.
Conclusion - all 7 vote

I did a test on HAB self-rels just because you had.
I improved HAB self-rel from +20.25 to +70.25, 5 tests all came out HAB wins
Conclusion - my base case does respond to improvements in HAB rels by swinging the result to HAB

I tested a few non-electors by increasing HAB's rels with them to +200 (just to make sure)
'Elector', Tests, Result
POL, 5 all KNI
SWE, 5, all KNI
FRA, 5, all KNI
Conclusion:
None of these vote.
Would I have got a HAB win if I'd gone on testing? After all, as long as these are all non-electors, this is the same as my base case which shows around 85% KNI wins. I wasn't sure so I did another 9 tests on FRA, and on the 14th test got a HAB win. This at least shows similar behaviour to my base case.

So, I'm about ready to declare that the mouseover electors are in fact the electors.
I think we need to settle this one.
I think you need to do a few ad hoc tests on your base case, by making larger modifications to the rels, to demonstrate that all mouseover electors can at least affect the result.

So far as non-mouseover electors being electors, are concerned, are there any you would like me to try other than the 3 above.
- I didn't bother with DAN, but could if you thought it worthwhile.
- Hungary has long been diplo-annexed by HAB in my game.
- I could do Spain, but since France isn't, I will only do so if you are doubtful. Similarly for Portugal, Venice and Tuscany
- The Papal States, Modena and Milan have all gone in my game
- I can't see the point in trying England. Scotland and Eire have both gone
- I can't see the point in trying Orthodox, Muslim or Pagan countries

However I'll try anything to be able to stop calling them mouseover electors and start calling them electors.
And obviously, with the level of effort that's going into this, we need to be sure, so another 20 tests won't hurt.

4) Whilst my mind was going numb with all these tests, it occurred to me that a very credible incumbency factor might be as follows:
The incumbent retains the emperorship, unless some critical threshold is achieved by another candidate in the election. Perhaps he has to get 2/3 of the electors (if it is a 1-elector-1-vote system), or a total rel above some figure. There are many possibilities.

The point being, of course, that this would be consistent with the behaviour we have seen:
- once somebody is HRE, somebody else has to do something pretty significant to get it, after that he tends to keep it
- it's also one possible way in which a relatively small reduction in rels for KNI results in losing the election, even when HAB isn't very popular

This would certainly put a different aspect on the various HAB results that we both get - they may not be a case of HAB winning, more a case of KNI (or GEN in your case) not 'winning'.
Worrying about this was why I decided to focus on some non-HAB, non-incumbent tests.

5) Eliminate any HAB and incumbency effects
I modified FRA and KNI rels to +200 for all 7 mouseover electors
I modified HAB to -200 for all 7
30 tests, FRA won 12, KNI 18.
Conclusions:
- It kind of looked like a 50/50 distribution as it was coming out. I don't know what the odds are of getting 12 heads on 30 tosses of a coin, but probably not outrageously improbable, so it might well be a simple even chance.
- FRA has Louis XIV, who is Dip 8 (high values ARE better dips aren't they?), and my KNI guy is only Dip 4. So the fact that KNI wins more than FRA at least might indicate that monarch dip rating is not a factor, or only a small one.
- It really does not look like candidate size/strength matters at all. On virtually any measure you care to look at FRA swamps KNI (which is tiny, one European province, 30,000 troops in total, a handful of colonies, a miniscule income etc. etc. I do have about the same number of diplo VP's as France, that's the only thing in the save file that is even remotely comparable.

Anyway this gives me a base case to try variations on, where neither are the incumbent or HAB.

6) As 5, but KNI +199 for all 7, FRA +200 for all 7
Results: 20 tests, FRA 19, KNI 1
Conclusions:
- This is a very very important result, and I've no idea at the moment how to interpret it!
- It may be suggestive that the election is on a count of 1 vote per elector, with random factors applied in some way before determining the elector's vote, but we know it isn't as simple as that.
- Equally, for me it rather throws out of the window any simple sum-of-rels-with-additions system

7) As 6, but the other way around
Results: 20 tests, KNI 19, FRA 1
Conclusions: As for 6. I only did it for rigour. The fact that it gave exactly the same result is pretty, but coincidental.

8) A bit like 5, 6, and 7, but rigged to ensure that one candidate has a slightly bigger rel for 6 out of the 7 electors, yet the total sum of rels is exactly the same. In fact the setup was:
Elector, FRA, KNI
HAB, +200, +199
PRU, +200, +199
BAY, +200, +199
BOH, +200, +199
PFA, +200, +199
SAC, +200, +199
BRA, +194, +200
You can see this accomplishes the objective. HAB was still -200 with everybody to keep them out of the picture.

Results: 20 tests, FRA 17, KNI 3

Conclusions:
- Is 17/3 suggestive of a different random effect than the 19/1 results we got in 5 & 6? Dunno. Not big enough test samples to be sure.
- Is 17/3 definitely different to the 18/12 results we got in 4. Yup, I'd say so. You have to watch them coming out to really feel the difference. In section 4, the results were dodging around between FRA and KNI, but turned out at 18/12. In this case it was all FRA, with the occasional surprise KNI win.
- Now 'feel' doesn't prove anything, but I'd definitely say that this further invalidates the simple-sum-of-rels-plus-additions theory

Would I have got a HAB result if I'd done a 100 tests on any of 5, 6, 7 or 8? Dunno. Setting them to -200 may be enough to make it impossible, or only enough to make it highly unlikely.

Next I'll play around with some more setups like 8.

 

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Great stuff! The BRA result may match my result of 15 as the random factor. Bear with me on this. Assume that 15 holds out as the random factor. Then your result shows a swing from a 50/50 result to a result close to 80/20 or so. My data show that this is pretty linear, so this change corresponds to a relative shift of about 5 relationship points. so -1 on each of the other 6 vs. -6 on BRA leads to a swing of about 5 relationship points which means that the BRA weight is roughly half of the average. There is a lot of uncertainty and I've made several hidden assumptions, but it could be consistent

Your approach is better than mine, but I'm going to keep attacking from my direction with guidance from your work. I have no other suggestions on other countries to test. I need to look at HAN, SAC, and PFA - the rest seem to count correctly in my tests.

And by the way, back to semantics my 'always wins" should be read as won 25/25 in my tests, which is not the same as always!

On the BRA result, an alternate explanation is that it's not the weighting of an individual elector that matters, but it's the exact number (so 200 vs 199 6 times is not the same thing as 200 vs 194 once). This would still allow equal weights. I can look back at the relations in my tests, but I don't think PFA, HAN, BRA and SAC are any different than the rest.

Also note that I've pretty much shown that incumbency is small, and that DIP doesn't seem to matter too much.

I'd recommend you repeat your last test for the different electors and maybe we can see which has the biggest weight. My data (that I haven't listed) shows that the function is linear, so the relations difference between 0% chance and 25% chance is the same as between 75% and 100%. So the relative probabilities should be identical to the weights (with statistical uncertanty of course).

edit: still trying to think straight

 

[Sharur]

Wow, this is comprehensive. I just have one small suggestion to make: why not open a game and save it on Jan 1, 1492, and then edit the death date of the Habsburg monarch to Jan 2 (or whatever), and run the tests from there? That way you'll eliminate any possibility of having unsaved factors affect the first save, you'll be able to test every country, and you'll both have basically the same file to work with.

 

[Chas]

Thanks. The tests you suggest are what I was thinking of - my guess going in is that it will make no difference which elector I set at 194, it'll always come up with the same result. Almost every guess I've made so far has been proved wrong, which is what's keeping this fun.

I need to understand better your hypothesis about how it might work.
Is this right:
- you are not sure how the election works
- but you do know that certain elections are close, 'cos we can contrive them, without quite knowing how
- At least in those cases where an election is close then a reduction of 15 rel points is enough to turn an 'always wins' into an 'always loses'
- Intermediate values produce statistically intermediate results
- it doesn't matter which elector you take the 15 points from, it has the same effect (actually I'm not sure whether this is your hypothesis, you seem to have been moving on this as the test results have been coming in)

You say

Then your result shows a swing from a 50/50 result to a result close to 80/20 or so. My data show that this is pretty linear, so this change corresponds to a relative shift of about 5 relationship points. so -1 on each of the other 6 vs. -6 on BRA leads to a swing of about 5 relationship points which means that the BRA weight is roughly half of the average

- If the function is linear, why wouldn't 6 x -1 cancel out 1 x +6 ? (obviously as it's random it would never exactly cancel out, but I mean on average, wouldn't 6 random factors of -1/15 cancel out 1 random factor of +6/15)?
- I don't follow the bit about BRA weight being half the average

Humour me with a longer-winded explanation.

Re Sharur's suggestion: It's not daft, though:
- of course we run no risk of unsaved factors affecting the results in our current save files, by definition. And running a 2nd Jan 1492 set of tests would still leave open the possibility of unsaved factors accumulating with time.
- we could always swap save files if we need to work on the same one. Just at the moment, when we (well, I, at any rate) are floundering around in the dark, I think it's better to have as much variety in the test data as possible, just for serendipity to work its magic. Once we have a good substantiated hypothesis we can think about standardising things. A test in Jan 1492 at that time might be a damn good idea. (Also, I have a lot less work to do with only 7 electors - if only HAB had dip-annexed BAY and BRA had dip-annexed BOH, as they do later in the game, it would be even easier!)
- whilst I'm pretty sure that religion doesn't affect things, we certainly couldn't test that in 1492, could we? I mean, I suppose you could change a religion in the save file to Protestant, but there wouldn't be Protestant on the sliders, would there?

 

[Sharur]

It seems to me that scientifically, the fewer the variables, the better, so not having to worry about religion would be a bonus. After all, wouldn't you want to get a general idea first, and then once you're got that test out other variables such as religion?

Also, how does a Jan 2, 1492 election allow any unsaved factors to crop up? That's just one day, and a couple of days are passing from your load point until the election in your tests, if I'm not mistaken.

 

[Chas]

Originally posted by Sharur
It seems to me that scientifically, the fewer the variables, the better, so not having to worry about religion would be a bonus. After all, wouldn't you want to get a general idea first, and then once you're got that test out other variables such as religion?

Also, how does a Jan 2, 1492 election allow any unsaved factors to crop up? That's just one day, and a couple of days are passing from your load point until the election in your tests, if I'm not mistaken.

Yes, fewer variables makes understanding things easier:
- there aren't many fewer variables in 1492 than in 1700 though.
- and part of the exercise is to discover what variables do influence things
- by freezing a base case and altering only one thing at a time, I think we are isolating variables anyway
- and serendipity is important

Unsaved factors:
- Of course, there probably aren't any, it's probably just a figment of my paranoia, I was just brainstorming things that might be going on
- Yes, your Jan 2nd 1492 system would avoid any cropping up
- But the system that Isaac Brock and I are using also doesn't allow them to crop up (I'm not so paranoid that I think anything significant is occurring in the 5 days between my save and my election)
- The point about unsaved factors, if there were any, is: If we ran a game without reloads from 1492 to 1705, would we get the same result (or more particularly, the same statistical set of results) as reloading in 1705 and running the election? Running elections in 1492 doesn't bear on this question - it doesn't make it worse or better, we are still running elections directly after a reload
- I'm not sure there is any way of testing unsaved factors at all. It's all too hypothetical. Over what period might they occur? It's simply impossible to run without reloads, because of crashes to the desktop, and needing sleep. It's impossible to guarantee that a game over a long period ends up with the same setup as a reload, because of all the valid random factors in the game. The best that could happen is that, assuming we get a replicable (on reload) theory of how elections work, somebody in real game play gets a contradictory result, and saves, and the save file shows the contradiction is unambigous (not a very likely thing to happen, given that we know that the elections have a random element anyway). Then we would know that there is something else going on, but I still don't know how you would work out what it is that happened. Which is why it is devoutly to be wished for that there aren't any.

 

[unmerged(6159)]

I think I agree with Chas here. Attack it from several directions, and hope to get lucky. It certainly avoids the danger of duplicated work, and if you haven't tried it running 25 tests of the exact same save is pretty boring.
I do agree with your points
-I certainly don't know what's going on.
-I think I know more thatn just that elections can be close - on the HAB scale I knwo how close
-15 points for MOST electors does seem to change an always wins into an alwys loses. However, I have come to accept your point that BRA must vote and in my save their vote clearly counts less then most other electors. Most of my tests show that it is symmetric, by which I mean that increasing the 'HAB always loses' save has the same effect as reducing the 'HAB always wins' save. With one exception.

When I say that it's linear I mean that if the 'HAB always wins' is 15 rel. points from 'HAB always loses' then the 'HAB wins 50% of the time' is exactly 7.5 points between them (of course I haven't proven this, but it makes sense and my data strongly support it). So from my tests if 15 points on HAB-BRA gets me to the point where HAB wins half the time I would assume that HAB-BRA gets half the weight of HAB self relations. For whatever reason imaginable. My immediate goal is to get the weights for all countries and see if I can spot a patttern.

I've done a few more follow up tests (I'm afraid I'm not as prolific as you, I get bored after 30 minutes to an hour and end up playing instead).
For HAN I changed the HAN-HAB by 30 point instead of 15. This gives the expected result. They vote. I suspect the one HAB win in my first test was a fluke - when you run 50 tests 1-2% chances start happening.
For PFA I have some very mysterious results which I will now tabulate

HAB self 	HAB-PFA		HAB wins	GEN wins
61		15.71		25		0
61		.71		7		3
61		-14.29		2		12

46		15.71		0		25
46		30.71		8		2
46		45.71		8		4

Everything else fits with some sort a weight format, but this is mysterious. It is clearly not symmetric, and the only case I've seen that isn't. It's not being reformed, because Hesse worked just fine. Anyone got a guess?

PS I guess PFA misbehaving in the 1619 election is probably pretty historic, but I'm assuming it's not hard coded for 1619.

 

[Chas]

1) Yesterdays last test was of FRA and KNI with high rels, and HAB out of the picture.
Specifically, the sum-of-rels for both candidates was the same, 6 electors had +200 with FRA and +199 with KNI, the 7th had +194 with FRA and +200 with KNI
The '194' elector was BRA
The result was FRA 17, KNI 3

I said I would try this pattern with different '194' electors
With HAB as the '194' elector, the result was FRA 12 KNI 8
Not sure if this difference is statistically significant relative to the 17/3 result above.

I then realised that I was doomed to uncertainty over any answers I might get, other than gross reversals of the pattern to KNI being the most frequent winner (which I am pretty sure would never have happened). I was very reluctant to embark on doing 100+ tests (which would eventually settle this question) as I have no real idea of what I am seeing here. So I stopped on this pattern at this point.

2) I then did some tests with a general pattern: Sum-of-rels the same for FRA and KNI. 3 electors with +150 FRA, +200 KNI (called 'to KNI' below), 3 the opposite way round (called 'to FRA' below), and one with both at +200 (called 'equal' below).

To FRA: HAB,PRU,BAY
To KNI: BRA,PFA,SAC
Equal: BOH
Result: FRA 17 KNI 3
Conclusion: Something is helping France out

3) Swap over BRA and HAB
To FRA: BRA,PRU,BAY
To KNI: HAB,PFA,SAC
Equal: BOH
Result FRA 10 KNI 10 (FRA 14 KNI 6 on a retest, see below, which gives FRA 24, KNI 16 in total)
Conclusion: Something has changed

4) Try to make KNI the winner - hypothesis that bigger/stronger electors have more sway
I did a European province count - most other measures go roughly in line with this. The province count for the electors is:
HAB 12
BRA 6
PRU,SAC 3
BAY,BOH,PFA 2
So I did:
To FRA: BAY,BOH,PFA
To KNI: HAB,BRA,PRU
Equal:SAC
Obviously this is giving the big countries to KNI and the little ones to FRA
Result: FRA 18 KNI 2
Conclusion: Collapse of hypothesis (Good old Karl Popper, science does indeed advance by the experimental disproof of hypotheses. Which is why experimenters have less nervous breakdowns than theorists)
What on earth could be causing the difference between 2 and 3? Started looking very carefully at the particular groupings that I had in 3.

5) Hypothesis: it's Bohemia that caused the different result in 3. Swap BOH with PRU.
To FRA: BAY,PFA,PRU
To KNI: HAB,BRA,BOH
Equal:SAC
Result: FRA 10 KNI 0
Conclusion: Collapse of hypothesis
Hmm, in all my tests I am only altering candidate rels, not the counterpart rel for the electors, something I proved to my own satisfaction was OK right at the beginning, maybe I was wrong.

6) As 5, but alter all the elector rels as well, to mmake the 'matrix' symmetrical
Result: FRA 10 KNI 0
Conclusion: Well, thank God for that I suppose, at least the 'candidate rels' theory holds up, but I'm still no closer to understanding 3.

I could think of no further combinations that would be worth testing to try and get the KNI win-rate up to, or even exceeding test 3.

7) Maybe I did something wrong in the 20 tests in test 3, do another 20.
You saw the results of the retest in 3 above, and they tend to confirm that test 3 is special

8) Then I started looking around the screens. In my base case, and all tests, the following relevant alliance is in place:
BRA leads an alliance with FRA,BOH,PRU. The alliance is at war
No other electors are in an alliance with other candidates.
Now this will make you go cross-eyed:
- What if FRA gets some bonus rels for each elector that it is allied with, but this bonus cannot push the effective rel over +200.
- In test 2 FRA is already +200 with PRU ('to FRA') and BOH ('Equal'). But the other member of the alliance, BRA ('To KNI' and therefore only +150 with FRA), would give FRA the benefit of the alliance effect - given that the setup is highly symmetrical, this would push things in FRA's favour
- In test 3 FRA is already +200 with all the alliance members, PRU and BRA are 'to FRA', BOH is 'equal'. So FRA cannot benefit from the alliance effect, so the symmetrical setup gives symmetrical results
- In test 4 FRA is already +200 with BOH ('to FRA'), the other alliance members BRA and PRU are 'to KNI'. So FRA benefits from the alliance effect on 2 electors
- In test 5/6 (same test really) also there are 2 alliance members that are 'to KNI' and would give FRA the benefit of the alliance effect

So the hypothesis is that FRA wins mostly wins this highly symmetrical case, because of the alliance effect. Only if FRA's rels with it's alliance partners are already maximum does the alliance effect provide no further advantage, and things ocme out roughly 50/50.

Well, it's a theory.

I note that BOH is a vassal of BRA but can see no potential effect of this in any tests so far - after all it's just 2 electors, no candidate involved.

Now, I can't really do much more testing on this base case to try out this theory. I would need to set up different alliances and see what happened. Quite a lot of work, and it would be nice to understand your own alliance position and whether this theory helps explain any of your results before I do. Can you post the alliances that HAB and GEN are in, assuming they include any electors/potential electors. Are any such alliances at war? Or better still, see 12 below

9) From your last post:
You say 'For HAN I changed the HAN-BRA by 30 point instead of 15'. Do you mean 'For HAN I changed the HAN-HAB by 30 point instead of 15'? Else I am really confused.

10)Re your mysterious PFA result:
- Possibly it's just sample size: 7/3 and 8/2 could be representative of 50/50. 8/4 for the 45.71 result is much harder to explain this way.
- With no very clear idea of how it might affect things, is PFA in a relevant alliance? e.g. If PFA is in an alliance with HAB, maybe the alliance effect is already giving it a maximum amount of benefit, and increasing HAB-PFA gives no further benefit. I'm not very convinced by this, it would be easier to speculate if I knew about your alliances
- I note from your earlier post that PFA is one of the few electors that GEN is strongly negative with. The others being BRA (which you have had slightly anomalous results for) and PRU. GEN is also not very strongly positive with HAN (which you have had slightly anomalous results with, and maybe the 1 HAB win wasn't such a fluke) and SAC (which I'm not sure about). For this explanation to be of any relevance, I'd expect your PRU results to be out of the ordinary as well - were they?

11)Haven't you done any tests with GEN-elector rels changed? (even ad hoc single tests?)

12) I'd love to take a closer look at your base case (either 46 or 61, doesn't matter) - any chance of zipping it and e-mailing it to me?

 

[unmerged(6159)]

9) Yes that was a typo. It's fixed.
11) Haven't doen any GEN changes yet. It's worth thinking about, but I was hoping it's symmetric
10) PRU is one of the well behaved electors (i.e., I got 5/5 on both of the tests). I'll report the alliances later, although I'm pretty sure GEN has an alliance with KOL, BAD, WUR, and BAY. I had that alliance most of the game. Maybe I'll try more PFA tests, but I'm itching to go after BRA too.

 

[Sharur]

Sorry if I'm interrupting/bothering you two, but I find this really interesting even if I don't have the time/patience to conduct the research myself. Good work so far!

To Chas: if it isn't too much trouble, I would recommend removing all alliances involving electors (in another copy of the save, of course). You might also end up having to take RMs into consideration too

 

[Chas]

Originally posted by Sharur
Sorry if I'm interrupting/bothering you two, but I find this really interesting even if I don't have the time/patience to conduct the research myself. Good work so far!

To Chas: if it isn't too much trouble, I would recommend removing all alliances involving electors (in another copy of the save, of course). You might also end up having to take RMs into consideration too

No bother to me.
Yes, I may do this soon, I know you think that removing as many variables as possible is the way to go. I have looked at all the various diplo relations and may post them, but it looks like only alliances are relevant (if those). e.g. KNI has RM's with most electors, HAB has one with SAC, and that's it. I've also listed who has CB's on who, and who is banning trade for who - again,nothing that intuitively seems to explain anything.

 

[Chas]

This post is almost entirely concerned with trying to get a broad understanding of how the electoral system works.

1) Electoral college?
The last post covered messing around with FRA vs KNI, in various setups in which the sum-of-rels were equal but the rels for indiviudal electors were assymetrical, or symmetrical giving assymetrical results. These showed that, when things are very close, it's not simple to explain behaviour on a sum-of-rels based system. This led me to consider a variety of possible electoral college systems, including:
- 1-elector-1-vote
- 1-elector-1-vote with bonuses to rels based on candidate characteristics (e.g. alliances) up to a maximum of +200
- Several votes per elector cast, say, 3 for the most preferred candidate 2, for the next etc.
- Systems in which the incumbent retains the vote unless a new candidate gets a majority of the votes (in my case 4 or more of the 7). Looking at the rels between my electors and all RC candidates, and using a bit of imagination about bonusing systems, it was possible to convince myself that HAB was winning when a variety of non-HAB non-FRA candidates were getting +200 rels

So I tried a few variants to see if this could be right:
- In my base case HAB-BRA is -138 and it's hard to see how any system could give BRA's vote to HAB, but it could conceivably go to FRA. So I reduced the FRA-BRA rel to -200 (now he can't win it either) and set KNI-BRA at +150 (this is a rel that would normally swing my base case from KNI wins to HAB wins, in this case I hoped that what would happen is that KNI now still gets BRA's vote, being miles ahead of the others with BRA)
Result: HAB wins 5/5
Conclusion: Another theory bites the dust. I am now (especially after all the other tests in this post) totally unconvinced by the alliance theory in the last post, though I still can't explain the results of the relevant test.

2) So I played around with a set of tests to see if sum-of-rels, at a gross level, accounted for things. By 'at a gross level' I mean a change of 50 rels. This would still leave the behaviour of close elections unexplained, but would constrain the set of possible explanations.

- Reduced KNI on 1 elector by 50 and reduced HAB on the same one by 50 - result: KNI wins 4/5, as expected by sum-of-rels behaviour
- Reduced KNI by 50 on one elector, reduced HAB on another elector by 50 - result: KNI wins 5/5, ditto
- Put KNI to -200 with all electors, increased FRA to +200 with all electors - result: FRA wins 9/10, ditto
- As previous, reduced FRA by 50 on 1 elector - result: HAB wins 5/5, ditto
- As previous, but a different elector - result HAB wins 5/5, ditto

So this really looks like simple sum-of-rels

3) How can it be simple sum-of-rels and HAB ever win?
In my base case the totals are KNI 1399.9, HAB 206.0, a difference of about 1200.
In Isaac Brocks base case the totals are GEN 1188.0 HAB 400.0, a difference of about 800
- This is using your '46' case
- It uses all 13 mouseover electors in the totals, I am now confident about these, see below

Now there are lots of ways that HAB could be getting 1200 rels in my case, including:
- a flat 1200 rel bonus that's just added
- a bonus of 170 rels added for each elector
- a bonus of 150 rels for each elector and another 150 for something diplomatic that we haven't fathomed yet
- and so on, endlessly
And there a lots of ways the bonus could be applied:
- Added to HAB
- Subtracted from other candidates
- Factoring up HAB's rels
- and so on, endlessly

BUT, no system I can think of makes any sense when you look at IB's case - he has more electors than me (13 vs 7), so any elector bonus based system will give more to HAB, not less.

So I figured, without knowing much about the setup in IB's case, that maybe HABs bonus is related to HAB's size/strength - you can see how the programmers might have wanted to prevent a situation where a 1-province Austria is still getting a prestige bonus intended to reflect history. I looked at Austria's provinces: it has 15 provinces, 13 of which it controls and 4 of which have shields. These numbers could quite possibly be factors to produce 1200, and maybe Austria is weaker in IB's game (in mine HAB dip-annexed Hungary early on, which doesn't always happen).

So I started taking provinces off HAB. At least, I'm pretty sure I did - I've never tried this level of save-file editing before. I removed the province number from the Owned, Controlled and National Lists, and deleted the relevant city in the city section. Advice please, is that enough? At any rate, this meant that the provinces showed up as neutral on the map, so I think it must have worked.
- In my base case I first took away Erz, a non-shield province, and set up a simple HAB-wins set of rels (reduced KNI-BRA to 150). Result: HAB wins 5/5, as normal
- I then also took away Silesia, a shield province. Result: HAB wins 5/5 as normal
- I then set HAB's BB from 0 to 10. Result: HAB wins 5/5 as normal

So I've now run out of things that might be better for HAB in my game than in IB's.
So I'm at a dead stop.

4) Try another election
Maybe HAB's bonus increases over the centuries, say from 400 rels in 1492, to 800 in 1592, to 1200 in 1692 etc.

I create another base case, at the same date as IB's, 1619. I won't go into detail, but:
- in game play HAB won
- all the RC's have lousy sum-of-rels (including KNI, I hadn't really got going on improving them at that time) except for HAB and POL which are both just positive (so you'd expect HAB to win every time easily)
- there are 11 electors

I then did a set of tests, increasing KNI's rels massively and adjusting to find out what sort of HAB bonus is being applied. This turned out thus:
Sum-of-rels HAB 36 KNI 1210 gives 10/10 KNI wins. Taking 100 off KNI gives 10/10 HAB wins. I could fine tune it closer than this, but it's somewhere around a 1200ish difference.
The 1210 for KNI comes from 11 electors at +110 each.
I call this my second base case.

In my first case, with only 7 electors left, anybody that beat HAB had to be at nearly maximum with all 7. This reduced the testing possibilities e.g. I couldn't add 100 rels to HAB and 100 to KNI to see if the results came out the same - there was no elector at less than +200 to add them to for KNI. In this case, with 11 elctors and only 1200 rels needed, there was much more room to play with, so I did some more sum-of-rels tsts:
- Set one elector for KNI to 0 and made the others +120 - result: 5/5 KNI wins, in line with sum-of-rels behaviour
- Set another elector at 0 as well - result: HAB wins 5/5, ditto
- Both the previous tests used electors that IB has laready determined are electors, next I substituted THU for one of them. THU is the only elector in my set of 11 that I had not already determined is an elector, that IB has down as a possible/probable/definite non-voter.
Result: HAB wins 5/5, in lime with sum-of-rels behaviur and showing that THU is an elector.
(The only one left now is WUR, which at last count I think IB thought was a non-voter. I have to say that I am absolutely convinced now that the mouseover electors are the electors and I'll eat my hat if WUR isn't as well - note that IB doesn't necessarily deny this, he's just testing for their effect on the random variation in close elections - of course, I'd have to buy a hat first, but that'd be more fun than the testing).
- I added 100 rels to HAB relative to the base case - result HAB wins 5/5, in line with sum-of-rels behaviour

Net of this exercise, still totally flummoxed.The second case is consistent with my first, in that a 1200 rels HAB bonus accounts for things, but hterefore both cases do not tally with IB's case. I don't really know what to try next:
- I'm reluctant to try any more close-election cases until I am at least confident of the general election system. It's too easy to start concocting far-fetched interpretations of results then devising sophisticated tests to try out the theories, especially in any electoral colege based systems
- Yet if it's not electoral college based, how do 800 rels for IB and 1200 rels for me produce the same results i.e. close elections?
- But all gross-change tests absolutely confirm the sum-of-rels approach. This is worth a few more words. Obviously it is perfectly possible in any constituency or electoral college system for huge changes in the popular vote to result in no change in the result, and vice versa. So if a constituency was won by a majority of 900 (say 1000 votes vs 100 votes in a 2 horse race) then 899 votes can be added to the loser and still no change. Equally, if 8 constituencies were won by 1 vote (say 1000 votes vs 999 in each of 8 2-horse races) then switching 16 votes out of 32000 is enough to swing the election from 8/0 to 0/8 (something we in England are very familiar with from our own election system). But it isn't that hard to test for this sort of behaviour in the HRE election, at least at the gross level. Over the last several posts, and partcularly this one, I believe I have tried all the tests that could
show this sort of behaviour.

I have speculated whether it's because IB's game has GEN as the human player and mine is with KNI (the programmers say, "we know the AI will only do certain things to win the election, but the humans may go at it real hard, so we ought to make it tougher for little countries to beat HAB than bigger ones, to stop things getting too far-fetched"). I so doubt this that I can't summon the energy to test it.

I've wondered if HABs bonus is elector size/strength based. I don't know how strong they are in IB's game, but we know that they all roughly end up the same way, the little ones stay little or add a province and then get eaten, the medium ones grow a little then shrink etc. It's tough to believe there's that much variation in IB's game (except for HAB itself which can go quite strong on occasion, and can be down to 4 provinces on others). Bear in mind any rational version of this idea requires IB's 13 electors to be weaker than my 7.

If I can work out how to use tables on this message board, I'll post my matrices of electors vs catholic candidates.

Has anybody got any ideas how IB's 13 elector case shows an 800ish HAB bonus and my 11- and 7-elector cases both show a 1200ish HAB bonus? Personally I'd even be grateful for a 'no'.