[EM] Your Vote Counts! (silly voting methods)

[Jan Kok]

The voting methods proposed below give very high probabilities to all
voters that "Your vote counts!" - as compared with most other methods
discussed on this list.

This post is really a reductio ad absurdum argument showing that
improving the chances that voters' votes "count" (change the outcome of
an election) is not a useful goal by itself.

Your Vote Counts Version 0 (YVC0):  Before the election, given N
candidates competing for one office, assign the integers 0, 1, ... N-1
to the candidates in arbitrary order.  Let the people cast their
ballots.  Count the total number of ballots cast, divide by N, and take
the remainder.  The candidate who was assigned that number is the
winner.  With YVC0, you are _guaranteed_ to affect the outcome of the
election just by casting a ballot!

If you object that it doesn't matter how you mark your ballot, then I
offer YVC version P:  Each voter can vote for 1 candidate (a
Plurality-style ballot).  The tallying process is as follows:  Choose a
first-round winner using YVC0.  Now count the number of ballots cast for
the first-round winner.  Divide that by N and take the remainder.  The
remainder indicates the winner according to YVC-P.  In this method,
there is a (N-1)/N chance that you affect the outcome just by casting a
ballot, and, if you cast a ballot, there is (1/N)*(N-1)/N chance that
your choice of candidate affects the outcome.

Another ("even better!") method would be YVC-A, which is like YVC-P
except that you use Approval-style ballots.  Then you can maximize your
chance that your vote affects the outcome to at least (N-1)/N by
"approving" all of the candidates.

The reason that the YVC methods are silly is that you can affect the
outcome of the election, but (if there are a significant number of
voters) you have no way of knowing how to vote or not-vote so as to
achieve your desired outcome.

Cheers,
- Jan