[EM] Majority Criterion poor standard for elections

[Juho]

On Oct 27, 2006, at 7:48 , Abd ul-Rahman Lomax wrote:
> it seemed to me that the algorithm was not explained, but if it  
> was, it was without the kind of overall description that makes it  
> easy to understand.

Ok, point taken. I'll see if I find something. At least dropping  
proposals like tied at bottom without verbal justification is  
difficult to read if one doesn't already have some familiarity with  
such tricks.

One quick explanation of tied at bottom would be that this rule  
allows voters who don't know if it would be strategically better to  
vote A>B>C or A>C>B to vote A>>B>C or A>>C>B (sincerely, depending on  
if they prefer B to C or the other way around). With the tied at  
bottom rule vote A>>B>C in a way says that C loses to B _and_ B loses  
to C and neither of them wins the other. This opinion is valid if A  
may win. If A can not win, then the sincere preference B>C steps back  
into the picture and may influence the outcome of the election.

Was this maybe closer to the better explanations that you expected?  
There are also other ways to describe the reasoning behind the tied  
at bottom rule. Maybe several explanations and discussions are needed  
to give a full picture of how the method and rules are intended to  
work (and where the benefits and potential problems lie).

>> They may however trust if the experts say that the method
>> works ok.
>
> Maybe. But getting that consensus of the experts.... not at all easy.

Well, it seems difficult to get the consensus of all the experts but  
on the other hand I see plenty of all kind of groups of experts  
saying even that on particular method X (IRV, Range, Approval,  
Condorcet,...) is the ultimate best method, and using their time to  
promote it. :-)

>>  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).
>
> Same is true of Range, a method easy to understand. People *are*  
> familiar with it. (except for weirdnesses like the 25% rule, if  
> that applies).

If you refer to unexplained heuristic rules with 25%, I agree. My  
target is to avoid any heuristics in the rules but sometimes one  
needs to allow some of it in. Some methods are quite free of  
heuristics, e.g. plain Range (without any additional rules) or some  
of the simplest ranking based methods. In the Ranked Preferences I  
was forced to sneak some heuristics in. The IRV like elimination of  
the last candidates for example is not perfect in my mind but it  
works still. Same with the tied at top/bottom rules. Maybe some other  
smaller details as well.

>>>> Votes 55: A>B>>C, 45: B>>A>C elect A (the
>>>> majority favourite) although the B supporters strongly disliked  
>>>> her.

> But given that C is what could be called an "irrelevant  
> alternative," we then wonder why B was not rated at zero by the  
> 55%. That B was *not* so rated, we must assume as deliberate. B was  
> not rated at zero because the 55% considered B an adequate candidate.

Ranking a candidate (insincerely) at tied bottom (corresponds to zero  
here) doesn't help that much in this method. A still won even though  
her supporters sincerely admitted that B was their second (much  
liked) favourite.

Also the B supporters can't do much damage with insincere votes.  
Voting 45: B>>C>A would have given the same calculation results.

> So you end up, if B wins, with a candidate whom *all* voters, as  
> the votes were presented, consider either adequate or the best.  
> This is an excellent outcome!
>
> Whereas if A wins, you have 45% of the votes who think that A is  
> almost as bad as C, someone whom everyone rejects. Not good. Divisive.

I agree that with Range-like thinking the utility of A is actually  
lower than that of B. This method respected the majority instead of  
Range-like utility. The reason is that this is he best I could do  
without sacrificing the ability to vote sincerely. The intention was  
to improve the achieved utility from that of the Condorcet methods by  
including strength of preferences in the calculation but without  
falling in the strategic voting problems of the Range methods (in  
contentious elections).

> I see much better procedures that don't lose the maximizing  
> characteristics of Range. Such as the proposal recently suggested:  
> if the Range winner differs from the Preference winner (possibly  
> with some additional criteria, conditions which indicate that it is  
> possible that the Range winner is not a good choice, the most  
> likely involving substantial non-rating of the Range winner), then  
> there is a ratification election *or* a runoff election.
>
> A runoff, one might argue, would just replicate the original  
> election and elect the Preference winner. But not necessarily. The  
> knowledge that there was this other candidate who was rated, on the  
> average, higher than the Preference winner could lead many people  
> to change their vote in the runoff.
>
> A ratification election or a runoff both guarantee that the result  
> has the acceptance of the majority, satisfying the intent of the  
> Majority Criterion, which is based on the principle of Majority  
> Rule and which is only a problem when implemented in a binary  
> fashion with more than two outcomes.

This looks like an attempt in a good direction (going down from range  
instead of going up from Condorcet like I did) but I can't yet see  
how it would be balanced enough to work in practice. Also methods  
like Approval have similar good characteristics like being able to  
give points also to candidates that wouldn't have a chance in  
plurality, and thereby making them e.g. more plausible winners in the  
next election. Approval might also be more stable. But I'll try to  
study also if range could be improved by adding some new rules to it.

Juho Laatu


		
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