[EM] Re: majority rule, mutinous pirates, and voter strategy

[Juho Laatu]

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 C
>> could always make counter proposals that would be supported 202 
>> against
>> 101 and A would need better speaking skills than X (or a cannon).
>>
> 	This doesn't make a whole lot of sense to me so far, perhaps because I
> 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