[EM] Election design

[Forest Simmons]

Great example!

A geometric example of this type involving the four major cities of
Tennessee can be found spread across several electowiki articles explaining
various election methods.

The example deduces the preference ballot of each voter from the assumption
that voter V would prefer (as Tennessee state Capitol, for example) city X
over city Y, if voter V lives geographically closer to  X than to Y.

It could be the choice of an Olympic venue rather than capitol location,
and the metric could be travel cost instead of distance as the crow flies.

This kind of geometrical preference deduction can be made for any election
embedded in a metric space of any kind, concrete like this one, or abstract
like a hypothetical Yee Disgram.

Warren Smith has several of them on his website.

The first time I saw such a geometrically derived ballot set forty years
ago, I was very surprised that election methods like Borda, Bucklin,
Copeland, Coombs, Hare, etc... all with reasonable heuristics, could give
so many conflicting results. I was well aware that Arrow and others had
given abstract examples showing the possibility of rock paper scissors
cycles ... but the existence of a planar distribution of voters
concentrated in four cities giving rise to a cycle of Euclidean distance
preferences was a big surprise to me.

Anybody who doubts the existence of the concrete reality of cardinal
ratings in some practical democratic decision making contexts should peruse
Warren's examples on rangevoting.org

Note that Kendall-tau is an example of an abstract metric on permutations
of candidates, i.e. possible finish orders. This Kendall-tau metric is the
one used for rating/scoring the possible finish orders in the Kemeny-Young
method.

How can we break the public imagination of democratic possibilities out of
its current narrowly confined prison?

More teachers like Joe Malkevich are needed ... many, many more .... very,
very sorely needed!

-Forest




On Sun, Sep 11, 2022, 10:01 AM Joe Malkevitch <jmalkevitch at york.cuny.edu>
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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