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

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

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

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

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.


Date: Tue, 28 Jan 2020 22:43:35 +0200
From: Juho Laatu <[hidden email]>
To: EM <[hidden email]>
Subject: Re: [EM] Arrow's theorem and cardinal voting systems
Message-ID: <[hidden email]>
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. Majorities are meaningful also in cardinal voting systems since each majority can win the election if they agree to do so.

BR, Juho





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

robert bristow-johnson


> On January 29, 2020 6:05 PM Forest Simmons <[hidden email]> wrote:
>
>
> 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.

>
>
>
>
> > Date: Tue, 28 Jan 2020 22:43:35 +0200
> >  From: Juho Laatu <[hidden email]>
> >  To: EM <[hidden email]>
> >  Subject: Re: [EM] Arrow's theorem and cardinal voting systems
> >  Message-ID: <[hidden email]>
> >  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.

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

C.Benham
In reply to this post by Forest Simmons

Forest,

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.

Is electing the CW (based on sincere full ranking) in your view always the "optimal result"?

Say the sincere ratings scores are

49  A99 >   C1 >  B0
03  C99 >   A98 > B0
48  B99 >  C2 > A1

If  we don't like the idea of electing  "utility loser" CWs, why even collect the information telling us they exist?  I don't understand why the quite simple Smith//Approval(ranked above bottom) doesn't
have some traction.  Under that method these voters would presumably just vote:

49  A
03  C>A
48  B

A is the voted CW and the "utility winner".  No problem.

Chris Benham

On 30/01/2020 9:35 am, Forest Simmons wrote:
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, so that the purpose of a Condorcet completion method is to find the most likely "true" social preference order. 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.

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

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.


Date: Tue, 28 Jan 2020 22:43:35 +0200
From: Juho Laatu <[hidden email]>
To: EM <[hidden email]>
Subject: Re: [EM] Arrow's theorem and cardinal voting systems
Message-ID: <[hidden email]>
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. Majorities are meaningful also in cardinal voting systems since each majority can win the election if they agree to do so.

BR, Juho





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

Kristofer Munsterhjelm-3
In reply to this post by Forest Simmons
On 30/01/2020 00.05, Forest Simmons wrote:

> 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, so that the purpose of a Condorcet
> completion method is to find the most likely "true" social preference
> order. 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.
>
> Also falsely assumed is that the CW's cannot be utility losers and that
> Condorcet Losers cannot be utility winners in any rational way.
>
> 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.

Although I'm more of a Condorcetist myself, here's a thought.

As I said earlier on the list, if honesty consists of you normalizing
the worst candidate to 0 and the best candidate to 1, and then giving
every candidate in between a rating according to lottery equivalence
(and you're risk-neutral), then there is one and only one honest rated
ballot. Call that a semi-cardinal ballot.

For semi-cardinal ballots, IIA reappears (since you get majority rule
with two candidates), but that there is only one honest ballot should
make the externalization/manual DSV complaints go away to quite some degree.

How well can we do with such ballots? What kind of strategy resistance
and utility performance can a semi-cardinal method attain? It seems like
there's a strong limit to how well a method can deal with strategic
exaggeration, in particular, but it might still be interesting to look into.

(Of course, there's also the problem that ordinary voters would probably
not take the effort of being honest in the definition above. But I can't
see any other way of reducing the honesty ambiguity short of going
directly to rankings.)
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Re: [EM] Arrow's theorem and cardinal voting systems (Juho Laatu)

Juho Laatu-4
In reply to this post by robert bristow-johnson
> On 30. Jan 2020, at 1.39, robert bristow-johnson <[hidden email]> wrote:

>> On January 29, 2020 6:05 PM Forest Simmons <[hidden email]> wrote:

>> 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?)

All combinations are possible, as Forest says. If votes are 2: A=2 B=1, 1: B=10 A=1, A is the CW, but B is the UW. And even if we expect voters to normalise their votes (= use both max and min ratings), we can (add two candidates to the votes and) have something like 1: C=10 A=2 B=1 D=0, 1: D=10 A=2 B=1 C=0, 1: B=10 A=1 C=0 D=0, where A is still the CW, and B is still the UW.

Of course it is quite typical that the CW is also the UW.

In competitive elections one may assume that rankings are typically more sincere than ratings.

>
>> 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.

I think "one person one vote" is ok in the proposed system. Everything fine as long as all votes look the same and have the same influence.

I note that one can arrange the cutoffs also in ranking style. I mean that the cutoff can be treated just as one of the ranked candidates, and such cutoffs (one or more) could give us additional information on "preference intensities". One could for example have a vote A > B > preferred_limit > C > D > acceptable_limit > E > F. If acceptable_limit "wins" the (purely ranked) election, maybe the election would be declared void or something. The rules could be also such that handling of "real candidates" and "cutoff candidates" would be somewhat different, e.g. so that losing to some cutoff would lead to some conclusions, without even considering possible cycles including that cutoff. (ffs, no good concrete proposals available from me)

>>> From: Juho Laatu <[hidden email]>

>>> 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?

The definitions and discussions have probably gone in cycles since Llull, Condorcet and Arrow, so I guess there is no need to put any special weight on who used what words this time.

>> 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?

Yes, there is no majority supporting any other candidate over the CW.

Juho


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