[EM] When will Approval Voting defeat a majority candidate

[Adam Tarr]

--- In election-methods-list at y..., Bart Ingles <bartman at n...> wrote:

...

 > Voter acceptability scale (sincere)
 >     100 70 0
 >    ------------------------------------------
 > 26%  A  B  C
 > 23%  B     AC
 > 51%  C  B  A

...

 > 26%  AB
 > 23%  B
 > 51%  BC

While it's easy to get fixated on Approval's "failure" to elect the 
candidate with a majority of sincere first place votes, Approval does an 
admirable job of maximizing the utility of the electorate in this case.  C 
is considered 0% acceptable by almost half the electorate, while every 
voter will be fairly satisfied with B.  If we cast A as Stalin, B as 
Washington, and C as Hitler, do you still think Approval failed?  Granted, 
that's a specious argument, but it does illustrate the degree to which 70% 
approval is significant.

A more even-handed way to analyze it is to look at the actual utility of 
each candidate:

Candidate A: 1*26% = .26
Candidate B: 1*23% + .7*(26%+51%) = .739
Candidate C: 1*51% = .51

And again, candidate B is clearly the winner that generates the most 
happiness for the electorate.  That should be what counts.  The fact that B 
finishes dead last in a plurality vote (and IRV for that matter) highlights 
the emphasis those methods place on first place votes; a misplaced emphasis 
in my opinion.  A utility analysis unambiguously backs up Approval's 
selection of the compromise choice.

As a final note, the "C B A" voters are not forced to insincerely rank 
their favorite candidate lower than another candidate, only even with their 
next choice.  So their vote does not constitute a betrayal or even a 
strategic vote.  It's a sincere vote, given the constraints of Approval Voting.

-Adam Tarr
atarr at purdue dot edu

Adam Tarr, Ph.D. Student
Purdue University
School of Electrical and Computer Engineering
atarr at purdue.edu
(765)743-7287