[EM] Election design

[Joe Malkevitch]

Dear Colin,

I am not sure what “truth” you are seeking.

Differing voting systems for different “contexts” makes sense.  Differing  systems have emerged because they have differing “properties” and to the extent that one might try to use a system with many desirable properties as possible, theorems like those of Arrow and Balinski-Young show that “perfect” systems don’t exist. This does not mean we cannot find a better system than using vote for one ballots and decide the winner using plurality. Agreeing on a better system is hard because of disagreements about what properties the system used should have as well as the fact that some systems require information and skills voters do not always possess.

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/
________________________________________
From: Election-Methods [election-methods-bounces at lists.electorama.com] on behalf of Colin Champion [colin.champion at routemaster.app]
Sent: Sunday, September 11, 2022 4:21 PM
To: election-methods at lists.electorama.com
Subject: Re: [EM] Election design

CAUTION: This email originated outside of CUNY.edu. Do not click on links or open attachments unless you recognize the sender and know that the content is safe. Never send login credentials, financial information, or sensitive information by email. Report suspicious email to reportspam at york.cuny.edu
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<mailto:jmalkevitch at york.cuny.edu>

web page:

http://york.cuny.edu/~malk/
----
Election-Methods mailing list - see https://electorama.com/em<https://urldefense.proofpoint.com/v2/url?u=https-3A__electorama.com_em&d=DwMD-g&c=yJ4UutiJRKf_XEsHUtOboHQQfLtKBfRC_OV2xJVGo18&r=7pxaWK0WuEo0HxsF_q5vQGhLPUOIFx_uY8ytjKVDVA4&m=KXBv3D7dyxGIFQ2iushBVl4Z17nhmvpq2GC6514UEyRhYX7wvLRd3LelsMVXsuIc&s=oocYRWg9zw9GnK_JdyQ8nH7DG8U8wGPGwjoSmDAu6Rs&e=> for list info