[EM] Majority Criterion poor standard for elections

[Juho]

On Oct 26, 2006, at 5:21 , Abd ul-Rahman Lomax wrote:
>> I at least made a try few mails back on the list with "Ranked
>> Preferences".
>
> Tried what? To satisfy the Majority Criterion while allowing  
> preference strength to influence the outcome?

Yes.

> I don't think it is possible.

I think it is. Not in the Range style but maybe if one treats the  
strength of preferences in a different way (and doesn't allow them to  
influence in "wrong" places).

> However, I found the description of "Ranked Preferences" to be  
> incomprehensible. It's *complicated*.

I agree that it is complicated. Please point out if there are some  
specific details that I didn't explain properly. The overall  
complexity can not be helped (except by dropping some of the rules  
like tied at top). Better description styles could be possible.

> I suspect that there might be a way of expressing it which is much  
> simpler, or maybe not. If not, forget about it. If I can't figure  
> it out with a few minutes of focused attention, the public will  
> *never* go for it.

I agree that most of the public will not bother to dive inside the  
voting method to see how it works. That is the same for many voting  
methods. They may however trust if the experts say that the method  
works ok. The voting process is however relatively simple and  
understandable. Just put the candidates (or the best of them) in  
preference order and add strengths to the preferences if you feel  
like that (basic (flat preference) ranked votes work also fine).

>> Votes 55: A>B>>C, 45: B>>A>C elect A (the
>> majority favourite) although the B supporters strongly disliked her.
>
> Let's express this in Range terms to see what it might mean.
>
> I'll assume that there are three candidates total, A, B, and C.  
> What has been expressed above could simply be represented by  
> assuming that there are four ranks. A preference gap of two ranks  
> is expressed by ">>". So the range ratings (Range 0-3) are:
>
> 55: A:3 B:2 C:0
> 45: A:1 B:3 C:0

Yes. Good mapping to Range.

> Hey, why did C even bother to run?

Just to help me in showing that there were more than one strength of  
preferences in each ballot (">", ">>").

> Anyway, this election, as stated, comes out to be (totals)
>
> A: 3 * 55 + 45 = 210
> B: 2 * 55 + 3 * 45 = 245
>
> B wins.

Yes. And the possible voter strategy (approval style maximised  
preferences) associated with this Range feature is one key reason to  
why I started looking for an alternative method that would be capable  
of expressing the strength of preferences but still allow voters to  
vote sincerely even in contentious elections (without fearing that  
some strategists will "spoil" the election results).

> B wins even more handily if the >> represents a greater gap.

In the Ranked Preferences method the difference between the  
preference strengths is actually quite big. It is close to the 55  
voters saying: "Do all you can to elect A or B. If it is certain that  
either A or B will win, then I want to say that I like A more than B."

>> Strong votes however have power in other circumstances since votes
>> 40: A>>C>B, 40: B>>C>A, 20: C don't elect the Condorcet winner C
>> since A and B supporters strongly dislike her. Social utility is
>> maybe not yet maximized but maybe improved??

> Badly polarized vote patterns often create weird results.

The intention was not to create weird results. One could claim that  
electing C (with a regular Condorcet method or with Ranked  
Preferences) would be weird since now (with the help of the  
preference strengths given in the ballots) we know that C was  
strongly disliked by 80% of the voters. Regular (flat preference)  
Condorcet is thus not the optimal method if you know also the  
(sincere!) preference strengths in addition to the ranking.

> I'd suggest coming up with a clearer explanation, with calculation  
> examples of the proposed method.

The explanation part I already discussed above. I'll send the  
calculation process of these two examples in a follow-up mail. See  
also the one example calculation that I posted right after the  
description of the method.

> Yet it is quite clear that it is necessary to consider preference  
> strength to get optimal election results

Ok, let's continue our studies.

Juho Laatu

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