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

Juho Laatu juho.laatu at gmail.com
Thu Feb 6 07:08:58 PST 2020

```> On 30. Jan 2020, at 1.39, robert bristow-johnson <rbj at audioimagination.com> wrote:

>> On January 29, 2020 6:05 PM Forest Simmons <fsimmons at pcc.edu> 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 <juho.laatu at gmail.com>

>>> 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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