Hello James,
Some further comments on the two tracks (= two scenarios on what mutiny may mean in elections). Sorry that the mail is long (maybe too long and difficult to read for those who have not followed the discussion).
Best Regards, Juho
On Mar 19, 2005, at 04:38, James Green-Armytage wrote:
============ track one ============...
one where we talk about dynamics of sequential mutinies and how the voters may stop the process already before the first mutiny when they see the votes and understand the rules of the game,I think your conclusions on the first track made all the sense, so let's consider them agreed.
Does this mean you agree that foresight of potential further mutinies is
likely to deter mutinies against Smith set candidates?
With the "considerable cost of mutiny" (to the mutineers and/or defenders and/or neutrals?) assumption you seemed to have, yes. People may however hope that it is someone else who has to give up and stop making mutinies, not me.
This deterrence applies also to non-Smith-set candidates, particularly since mutinies after entering the Smith set are in the two examples easier than before entering the Smith set (and results of a mutiny requiring hard work could easily be lost to another easier mutiny). There are however other psychological reasons, like no risk of beaten captain taking part in the cyclic majority revolutions, why people may be more eager to attack them, as you pointed out.
Does it mean you acknowledge that this foresight will not necessarily protect non-Smith candidates?
As mentioned above, there seem to be both reasons that support and are against this. I don't have a 100% clear picture of all possible mutiny scenarios and their psychological impacts so that I could now give a firm opinion on the strengths of different mutiny cases.
Does it mean you agree that candidate Z (the non-Smith Condorcet loser)
is likely to be the most mutiny-vulnerable candidate in my RSTZ example?
Not yet. I'll make one question to understand your thinking.
Case 1: The voting method elects Z. R, S and T supporters make an agreement to replace Z with (e.g.) R and then forget further revolutions.
Case 2: The voting method elects R. S and T supporters make an agreement to replace R with T and then forget further revolutions.
Revolution of case 2 is easier to implement (if margins are used to measure difficulty of revolutions) and S and T have the motivation. Would that make R more vulnerable to a mutiny than Z?
- after the mutiny situation is about the same in both cases ("cycle of three")
- before the mutiny situation was not satisfactory to any of the mutineers
- the candidate that was replaced may feel more angry or more beaten after the mutiny
- mutineers may feel more or less ready for new mutinies after one revolution
- I didn't evaluate the possible cost of mutinies in this example
- I didn't address the possibility of R, S and T being members of the same party (clones?) => separate parties that don't like each others so far
I tried to construct this example so that it would help me seeing the difference between the "foresight" based mutiny tendencies that you brought up and the simpler mutiny tendencies that I used (mainly for track 2, but in interesting in track 1 too). So, if you find the rest of my comments repetitive or otherwise less interesting, clear comments on how you see the difference between these two cases might help me forward.
Does it mean you are willing to abandon the claim that minimax(margins)
winners are less vulnerable to mutiny than Smith winners, when they differ?
We are now on track 1 and that claim addresses track 2. I believe it is valid there. I don't want to claim anything on track 1 yet.
I identified also some possible additional scenarios:
- An alternative model where the cost of mutiny is low and therefore
mutinies could continue forever (instead of stopping when pirates
understand that the cost of mutinies is too high). Accepting one of the
Smith candidates to take permanent lead may thus be more painful than
"sharing the leadership" by making continuous mutinies.
In real life government/election scenarios, the cost of mutiny is always
high.
Yes, in government level elections. But there are also other cases. In track 1 we talk about possibility of continuous mutinies/elections. Therefore track 1 is maybe not the best model for large elections where cost of new rounds is high (e.g. normal presidential elections). I guess we are more likely talking about some smaller elections when talking about track one. If we are talking about election of a captain of a pirate ship, then cost of mutiny could be human lives, which is high (well, maybe some pirates do not value human life very much). On the other hand the pirates could be civilized or we could talk about electing a new chairman for a board. In these cases the cost of mutiny would be only few pieces of paper for the ballots and 15 minutes of time, and maybe some disappointments.
- B and C could join forces and make just one revolution where A would be changed to C (202 against 101) and stop there.
You suggest that the B>C>X>A and C>A>X>B pirates may join forces to
change A to C. In forming this coalition, the B>C>X>A pirates would
promise the C>A>X>B pirates that they would not mount a further mutiny
against C. But why should the C>A>X>B faction trust them on this, mutinous
pirates that they are?
In politics deals like this are very common. Pirate style politicians that are not trustworthy may also exist. I think the stopping problem is pretty much the same in all scenarios => deals, getting bored, risk of further revolutions eating the benefits and cost of mutinies may stop them.
Once the first mutiny has occurred, the B>C>X>A pirates could join forces with the disgruntled A>B>X>C faction, to get their man B at the helm.
Yes, but there are also some limiting factors like the deal and other reasons listed in the previous answer, and the fact that B supporters already have their second best alternative as the captain.
To be fair, I acknowledge that some mutinies might have more "sticking
power" than others. I suggest that this will depend on the strength of the
preferences involved, and so I suggest that cardinal pairwise may do
better in this sort of situation than any strictly ordinal method.
Yes, and cardinal pairwise style methods could at least in theory dig some additional useful additional information out. (Sorry, haven't made good enough analysis of it yet to give better comments but the basic idea seems sound.)
One more generic comment: The reason why I don't feel comfortable with track one style voting methods that may consist of two or more rounds is that when the voting behaviour of the earlier rounds is known, the possibility and probability of strategic voting increases, the need to defend against them increases, and the more probable it becomes that we don't get the sincere votes and the algorithm can not pick the sincere (= best candidate based on the agreed targets of the election) winner.
============= track 2 =============
...and another one where we try to do the decision just once and then live with the result until the next election day (few years ahead).Captain A would have more problems driving her policy through since CThis doesn't make a whole lot of sense to me so far, perhaps because I
could always make counter proposals that would be supported 202 against
101 and A would need better speaking skills than X (or a cannon).
don't understand the scenario. To begin with, we're assuming that there is
an extremely strong sincere cycle in the initial vote. I doubt that this
will happen very often (probably never to the extent of your example), but
I can accept the premise for the sake of argument. But then, are we
assuming that there would be a comparably strong cycle in the sincere
preferences of the voters on most public issues? I think that this is much
less probable.
Example of a possible real life strong cycle:
- candidate A spends 70% of her campaign time to talk about low taxes and 30% of her time to talk about good social security
- candidate B spends 70% of her campaign time to talk about good education and 30% of her time to talk about low taxes
- candidate C spends 70% of her campaign time to talk about good social security and 30% of her time to talk about good education
- 33% of the voters are unemployed and they want good social security. They vote C>A>B.
- 33% of the voters are students or academic and they want good education. They vote B>C>A.
- 33% of the voters are factory and office workers and they want low taxes. They vote A>B>C.
Conclusion: The selected strategies of three candidates lead to a strong cycle in the votes although the voters themselves are sincere and as normal as they can be. Strong cycles are quite possible in real life (although not usually as common and strong as this example tries to demonstrate).
If strong sincere loops are not probable, then defending against some strategies is maybe not needed. Same comment about strong loops that are a result of strategic voting.
Let's dump the pirate metaphor for track 2, and start talking about actual government institutions. Is A the president now?
My claim was that if low risk of mutiny (in the sense of track 2) is selected as the main target of the elections, then X should be the president. But let's continue commenting with A as the president. That doesn't make any difference here I guess.
What do you mean,
"problems driving her policy through"? Is the president supposed to write
legislation, and then rely on a popular ranked vote to have it passed? Who
says that the president has to win the vote on every issue? If A is
president, but the X faction wins the vote on several issues, that's fine
with me.
Ok, there is no clear relationship between the voting results and opinions on some individual questions. The president could get varying support to her different initiatives.
But on the other hand one can claim that politicians represent some certain set of values and voters tend to pick their side and then sympathize with their chosen candidates in many questions. Maybe they even rely on their favourite so much that they change some of their old opinions in line with what their favourite candidate says. Politics may thus get very personalized.
In this case "mutiny" might demonstrate itself in the form of public demonstrations. Former presidential candidate C could arrange a campaign against the policy that president A drives. She would be able to collect 10% of the 202 voters that support her criticism in a public demonstration against C's policy. C would get 10% of the 101 participants that support the opposite view in the counter demonstration in the following day. TV watchers would notice that C had 10 more people in the demonstration than what A had (is this a good measure of the strength of the mutiny?). Based on this they would make their conclusions on whether A is a strong mother of the country or a loser. Rest of the term of A would either suffer or benefit of the conclusions that people made.
One general (maybe clarifying) comment on track 1 vs. track 2: To me the main difference between these two tracks is that in track 2 the target is a "one shot election" where the (hopefully sincere) votes of the voters will be evaluated and winner decided. Track one seems to contain the possibility that voters could change the result of the election by arranging a new election (of all candidates) or a revolution (where x will be replaced with y).
=========== annex ===========
ANNEX 1: The pirate example.
101: a>b>x>c 101: b>c>x>a 101: c>a>x>b 100: x
ANNEX 2: The RSTZ example.
Preferences: 35: R>S>T>Z 33: S>T>R>Z 32: T>R>S>Z 71: Z>R=S=T Pairwise comparisons: R>S 67-33 S>T 68-32 T>R 65-35 R>Z 100-71 S>Z 100-71 T>Z 100-71
---- Election-methods mailing list - see http://electorama.com/em for list info
