[Election-Methods] Challenge: Elect the compromise

Fri Aug 24 06:53:55 PDT 2007

Hi,

Although Jobst may not have intended this assumption, I will continue to 
make the assumption that the B minority's preference intensity for the 
compromise C over A is much greater than the A majority's preference 
intensity for A over C. (I am NOT saying there is a way to measure or 
compare sincere preference intensities or utilities suitable for input 
into a good vote tallying algorithm.)  Without an assumption like this, 
we would have no reason to believe C is better than A for the society.  
There would be little motivation to take up Jobst's challenge to find a 
voting method that will elect C instead of A.  In other words, I believe 
we should confine ourselves to solving the "Tyranny of the Nearly 
Indifferent Majority" but not try to solve the "Tyranny of the 
Passionate Majority."

In the real world, it is much easier to elect a compromise than Mr. 
Lomax seems to be saying below, because in the real world the set of 
alternatives is not fixed to {A,B,C} by nature (nor by Jobst).  Most 
procedures allow a very small minority to add an alternative to the set 
being voted on. (Under Robert's Rules of Order, for instance, only two 
people are required: one to propose alternative D and the other to 
"second" the proposal.)

Suppose D is an alternative that is very similar to the compromise C, 
except D includes something "extra" that at least 11 of the A faction 
will like enough to prefer D over A.  Assume the extra in D is not so 
bad for the B faction that the B faction prefer A over D.  Then at least 
56 (45 + 11) have an incentive to add D to the set of alternatives.

The preferences in the 6 pairings of {A,B,C,D} would be as follows:
     A>C 55
     A>B 55
     C>B 55
     D>A 56+ (45 plus at least 11)
     D>B 55
     C?D  ?

The C versus D pairing is unspecified.  If D entails some transfer from 
the B faction to members of the A faction, then presumably all of the B 
faction prefer C over D.  We don't have enough information to say 
whether more than 11 of the A faction will prefer D over C.  However, we 
do know that the D>A majority will be the largest or second largest 
majority, so A would not be expected to win given a good Condorcetian 
method (such as MAM).

In some circumstances, the "extra" that amends C to D might be a vote 
trade: a promise by some members of the B faction to vote later in a way 
the 11 members of the A faction will need later.  Assuming this 
electorate will vote on many issues (or expect to have other important 
dealings with each other) and that it will not be kept secret how each 
person votes, the individuals will have an incentive to keep their 
promises.  In the case of a secret ballot, which undermines the 
incentive to keep one's promises about voting, the "extra" would need to 
be explicitly included in D to be credible.

The elections of greatest interest to me--and to most members of this 
maillist, I believe--are the election of people to public offices.  
Candidates and potential candidates are relatively free to advocate 
whatever set of policies they believe will maximize their chances of 
winning, especially if they've consistently advocated those policies or 
similar ones.  Given a competition-promoting majoritarian voting method 
such as MAM, why would candidates who want to win advocate a collection 
of policies A, when there exists a collection of policies D preferred by 
a sizable majority of the voters?  They would expect A to be a losing 
position, since potential candidates can enter the race at positions like D.

--Steve

-----------------------------------
Abd ul-Rahman Lomax wrote:
> At 03:32 PM 8/22/2007, seppley at alumni.caltech.edu wrote:
>   
>> The problem is not well-posed, since the sincere ratings are not expressed
>> in units, which means it's unclear whether C has the most utility for
>> society.
>>
>> However, assuming the intensity difference between the A faction's 100 and
>> 80 is much less than the intensity difference between the B faction's 80
>> and 0, here's another way to elect C: The 45 can pay 6 of the A faction to
>> vote for C. (Not necessarily a payment of money.)  We can expect members
>> of the A faction to be willing to sell their votes fairly cheaply since
>> they like C nearly as much as they like A, and we can expect members of
>> the B faction to be willing to pay that price, since they like C much more
>> than they like A and they can share the cost.
>>
>> (From an economics standpoint, transfers of wealth are not inefficient,
>> all else being equal.)
>>     
>
> That's correct. It is doable. It might also be illegal, here. But 
> there could be ways to do it legally, as mentioned, it would not 
> necessarily be a payment of money. But for these factions to trust 
> each other could be a problem. If C is elected, what is to keep the B 
> voters from simply not paying?
>
> Nevertheless, that kind of proposal is similar to what I mentioned 
> about systems that would encourage voters to vote true utilities. In 
> this case, the B supporters shift the utilities of some "selfish A 
> voters" so that they, selfishly, will change their votes. To pay the 
> minimum, the B voters could auction off the right to receive 
> payments, which payments would be conditional on C winning. Since the 
> A voters are, as described, selfish, some would sell their votes 
> fairly cheaply.
>
> Technically, they are not selling votes, they are bidding an amount 
> that they would receive if C wins. For them, it is like a hedge. The 
> bidding is in reverse, that is, it starts high and comes down. It 
> deserves more thought...
>
>
>   
>> --Steve
>> --------------------------------
>> Forest S replied:
>>     
>>> Under strategic voting with good information, any decent deterministic
>>> method (including Approval) would elect the Condorcet Winner A .
>>> Uncertainty as to the faction sizes could get C elected, but not
>>> necessarily.
>>>
>>> So some randomness is essential for the solution of this problem.
>>>
>>> The indeterminism has to be built into the method in order to make sure
>>> that it is there in all cases.
>>>
>>> Jobst's D2MAC would work here because the compromises' 80 percent
>>> rating is above the threshold for sure election when the two faction
>>> sizes differ by ten percent or more, if I remember correctly.
>>>
>>> If the compromise had only a 60 percent rating, for example, optimal
>>> strategy might give A a positive chance of winning.
>>>
>>> It is paradoxical that randomness, usually associated with uncertainty,
>>> is the key to making C the certain winner.
>>>
>>> Look up D2MAC in the archives for a more quantitative analysis.
>>>
>>> I hope that this doesn't prematurely take the wind out of the challenge.
>>>
>>> Forest
>>>
>>>       
>>>> From: Jobst Heitzig <heitzig-j at web.de>
>>>> Subject: [Election-Methods] Challenge: Elect the compromise when
>>>>      there're        only 2 factions
>>>> To: election-methods at lists.electorama.com
>>>> Message-ID: <445065910 at web.de>
>>>> Content-Type: text/plain; charset=iso-8859-15
>>>>
>>>> A common situation: 2 factions & 1 good compromise.
>>>>
>>>> The goal: Make sure the compromise wins.
>>>>
>>>> The problem: One of the 2 factions has a majority.
>>>>
>>>> A concrete example: true ratings are
>>>>   55 voters: A 100, C 80, B 0
>>>>   45 voters: B 100, C 80, A 0
>>>>
>>>> THE CHALLENGE: FIND A METHOD THAT WILL ELECT THE COMPROMISE (C)!
>>>>
>>>> The fine-print: voters are selfish and will vote strategically...
>>>>
>>>> Good luck & have fun :-)
>>>>
>>>>         
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