[EM] Election design

[Colin Champion]

Well Joe, my response is less enthusiastic than Forest's. I think you 
should purge your mind of anything you've learnt from Arrow. What's 
missing from your account (and from Arrow's theorem) is any reference to 
truth: you don't ask which is the right answer, or what makes it right, 
or whether the discrepancies are due to bad luck or to the unreliability 
of the voting methods.
    This is not to say that the right answer can be seen by inspection - 
it depends on context. In my view, if the ballots are rankings in a 
figure-skating competition, then the Borda winner is probably right, and 
if they are rankings in a referendum for minimum driving age, then the 
Condorcet winner is almost certainly right. There are harder examples in 
which different Condorcet methods give different results. The contextual 
information needed to identify the rightful winner then becomes highly 
specific, and the task of recognising the rightful winner almost 
impossible. If you see the problem in terms of the relationship between 
voting methods and truth, then it is hard but intelligible, while if you 
see it as a collision between arbitrary voting methods and arbitrary 
principles, then it is fertile in nothing but paradox.
    You've given me a pretext to jump on my favourite soap box... so I 
stop here.
       CJC

On 11/09/2022 18:00, Joe Malkevitch wrote:
> Hi:
>
> This post is a reaction to recent list discussions.
>
> The  election below (highest rank at the left) shows the votes of 55 voters who produced ballots without ties or truncation, putting  to the side if ballot rules allowed indifference or truncation. I designed this example for students in various mathematics courses that included some attention to mathematical modeling to explore the notion of the will of the voters.
> The method used to decide the election matters for the result.
>
> 18 votes ADECB
> 12 votes BEDCA
> 10 votes CBEDA
>    9 votes DCEBA
>    4 votes EBDCA
>    2 votes ECDBA
>
> If you use the ballots to choose a single candidate to win using:
>
> Plurality
> Run-off between two candidates with largest number of first place votes
> Sequential run-off (IRV)
> Borda
> Condorcet (Select candidate who can beat all others in a 2-way race if there is one)
>
> You discover the he 5 methods yield 5 different winners!
>
> The backdrop for this example (and others in its spirit) are the theorems of Arrow, Satterthwaite and others that relate election methods to “desirable and fairness” properties.
> It also relates to the issue of the skills real world voters can provide via “honest” ballots and how one should design elections which involves the choice of ballot type and the system used to count the ballots. There is also the issue of how the voters get information about the candidates and use this information to fill out there ballots. Polls whose accuracy is hard to be sure of often seem to be more important in how some voters vote rather than what the candidates stand for. What one does also depends on what “objective function” is being used.
>
> Regards,
>
> Joe
>
>
> ------------------------------------------------
> Joseph Malkevitch
> Department of Mathematics
> York College (CUNY)
> Jamaica, New York 11451
>
> My email is:
>
> jmalkevitch at york.cuny.edu
>
> web page:
>
> http://york.cuny.edu/~malk/
> ----
> Election-Methods mailing list - see https://electorama.com/em for list info

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