[EM] Fwd: Question about Limited Voting

[LAYTON Craig]

Probabilities are not easy to calculate in voting.  It all depends on the
particular limited vote rules, and the preferences of the voters.  Okay,
party A has 60% support, B 20% support and C 20% support.

If each voter votes three times, and each voter only votes for their own
party, then the best strategy would be for party A to run 5 candidates, and
parties B and C to run three.  Limited voting assumes that the parties use
some kind of strategy in determining how many candidates they run.

There are three possible results.  The first is that party A wins 5 seats.
This would happen if their spread of votes is fairly even between
candidates.  This seems the most likely result, as the spread doesn't need
to be perfectly even in order for A to pull this off (say, 50:43:40:25:22).
The second is that party A wins four seats, and there is a tie-breaker
between candidates B1, B2, B3, C1, C2, C3.  This also seems to be a fairly
likely result, as the spread of votes in a party is usually very uneven.
The third is that party A wins three seats, and there is a tie-breaker for
the last two seats between B1, B2, B3, C1, C2, C3 and any party A candidates
who got exactly 20% of the vote.  This could elect any combination of
candidates (with at least 3 A candidates).  This would only happen if voters
mainly voted straight down the ticket (which could happen), so that most A
voters vote A1, A2, A3.

However, if parties B and C decide to trade preferences, the results could
be rather different.  Either both parties would run one candidate and
instruct voters to vote for both candidates (if you're allowed to cast less
than three votes) or parties would run two candidates and instruct voters to
vote for both their candidates and the candidate on the top of the other
parties ticket.  If the voters are loyal, there are three likely results;

Party A knows about this vote trading in advance.  They run only four
candidates, then Party A would win four seats and B1 and C1 would have a
tie-breaker for the final seat.

Party A doesn't know about this in advance, and runs 5 candidates.  They
could still scrape in with four seats, if one candidate gets very few votes,
and the spread is very even between the others, but it is very likely that
they would get three seats, and B and C would get one each. 

It is impossible to put a percentage on the likelihood of any of these
results acutally happening, but I think that it's clear that a number of
unusual things would have to happen in order for A to have 3 members, and B
and C have one each, and thus it is fairly unlikely.  It is possible for
voters to vote straight down the ticket (and in some places this is very
common).  This is really the only way that this result could happen.  If,
however, your electoral system includes rotated ballots, then it is
increasingly unlikely.

-----Original Message-----
From: donald at mich.com [mailto:donald at mich.com]
Sent: Thursday, 26 October 2000 22:24
To: [EM]
Cc: Abaughm at aol.com
Subject: [EM] Fwd: Question about Limited Voting


  ----------- Forwarded Letter ------------
From: Abaughm at aol.com
Date: Wed, 25 Oct 2000 22:36:20 EDT
Subject: Fwd: Question about Limited Voting
To: donald at mich.com

From: Abaughm at aol.com
Full-name: Abaughm
Date: Wed, 25 Oct 2000 22:02:15 EDT
Subject: Question about Limited Voting
To: CVDUSA at aol.com

I was wanting to know how to compute the probability of a candidate from
each
group of  voters being elected.  I have three populations of  60%, 20%, and
20%.  There are 5 seats and a person can vote for 3 candidates.  I actually
need to know the probability of voting in 3 from the 60% and 1 each from the
20%.  Thank you.

- - - - - - - - - - - - - - - - - - - - - - 10-26-00
Dear Abaughm,
     I have forwarded your question to the Election Methods discussion list.

Regards, Donald Davison