[EM] Election design

[Joe Malkevitch]

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/