RandElect

[Clay Shentrup]

http://scorevoting.net/RandElect.html

I'd like to see this added:

Given that a majority winner exists (a candidate favored by 50% + 1), how likely is that candidate to be the winner with system X?

I'd especially like to see this for approval.

[Warren D Smith]

A majority winner would exist with probability zero in
the random elections model with infinite number of voters,
C>=3 candidates.
(WIth large but finite #voters, exponentially near zero,
one could prove using Chernoff bounds.)

So any naive simulation would fail.

One could artificially amplify the voters who voted Nixon top,
though, to get Clay's desired conditional probability.
And then I would think that Nixon would win with limit probability 1
in those scenarios with almost all the usual voting systems
and honest voting.
Certainly with plain plurality, score, IRV, condorcet, Borda, and
median-based score
his win probability would be 1, one can easily prove.


--
Warren D. Smith
http://RangeVoting.org <-- add your endorsement (by clicking
"endorse" as 1st step)

[Clay Shentrup]

On Saturday, February 7, 2015 at 1:37:46 PM UTC-8, Warren D. Smith (CRV cofounder, http://RangeVoting.org) wrote:

A majority winner would exist with probability zero in the random elections model with infinite number of voters

Then this model clearly sucks. If you were doing an issue-space model, you'd surely get plenty of cases where some extremists garner scant support and are crushed by some relative centrist. 

[Warren D Smith]

well, the RandElect model does "clearly suck", I guess... it is a very simple
model, just random-normal utilities. Not very realistic, but simple to define.

I do not think I'd use the phrase "clearly sucks" since it actually it
not bad quite a lot of the time. However, for other purposes, it
clearly shows its limitations, for example the fact a majority winner
happens with probability-->0 with 3 candidates in this model.