[EM] Arrow's theorem and cardinal voting systems (Juho Laatu)

[robert bristow-johnson]

> On January 29, 2020 6:05 PM Forest Simmons <fsimmons at pcc.edu> wrote:
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> Juho,
> 
> I always appreciate your comments, and I agree 100 percent with your point of view on this topic.
> 
> Unfortunately there are some Condorcet enthusiasts who believe that majority preference cycles can only occur from mistaken judgment among the voters or from insincere voting,

i don't assume that.  i believe that it is possible that sincere voting can possibly result in a Condorcet cycle.  but i think it will be extremely rare in governmental elections.  because i believe that normally a relatively small portion of voters for Nader will choose Bush as their second choice over Gore.

> so that the purpose of a Condorcet completion method is to find the most likely "true" social preference order.

the *real* purpose is this: to unambiguously establish in law what will happen if there is no Condorcet winner.  so that if such happens, everybody knows what the rules are and any squabbling should be resolved quickly by election officials and not need a judge in a court of law.

> It's a fairly innocuous assumption and can serve as a heuristic for coming up with ideas for breaking cycles, but it is not a solid basis in itself for choosing between methods.
> 

but many decent methods (Tideman, Schulze, even STV-BTR) don't need a completion method.  they have a consistent method that results in a winner assuming there are no tied vote counts in any intermediate runoffs.


> Also falsely assumed is that the CW's cannot be utility losers and that Condorcet Losers cannot be utility winners in any rational way.
>

a question: if there is a CW *and* assuming sincere ranking by every voter, is not the CW **always** the utility winner?  (or are you assuming varying "preference intensity" here?)
 
> These considerations make it clear that for optimal results relative to many applications the method must take into account preference intensities, which is why my favorite methods tend to be based on rankings with approval cutoffs if not outright score ballots.

but that is inconsistent with "One Person, One Vote".  even if i **really** prefer my candidate a lot and you prefer your candidate only a little, you vote counts no less (nor more) than my vote.  this is, in governmental elections, fundamental.

and, of course, in score voting voters are asked to make a tactical decision about how much to score their second choice and, perhaps, their third choice.  voters are not Olympic figure skating judges.  they should not have to be burdened with this judgement.

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> > Date: Tue, 28 Jan 2020 22:43:35 +0200
> >  From: Juho Laatu <juho.laatu at gmail.com>
> >  To: EM <election-methods at lists.electorama.com>
> >  Subject: Re: [EM] Arrow's theorem and cardinal voting systems
> >  Message-ID: <3B8A6FF5-0AFC-498C-ABED-95A516B0B32C at gmail.com>
> >  Content-Type: text/plain; charset=us-ascii
> >  
> >  My simple explanation to myself is that group opinions may contain majority cycles (even if individual opinions do not). This is to me a natural explanation that covers most of these social ordering and voting related (seemingly paradoxical) problems.

it's a quite elegant way to put it and i might appropriate this and make use of it in my discussions here in Vermont.  shall i credit you, Juho?

> Majorities are meaningful also in cardinal voting systems since each majority can win the election if they agree to do so.

well, that's true for each majority involving the CW.  isn't that what the CW is?  for pairs of candidates where neither is the CW, those majorities should not win the election, because if any does, there is another majority that is losing.  assuming there is a CW and assuming all votes are sincere, then there is only one consistent majority winner.

--
 
r b-j                  rbj at audioimagination.com
 
"Imagination is more important than knowledge."