APPENDIX 6: VOTING IN SINGLE MEMBER CONSTITUENCIES AND THIRD PARTIES

                         APPENDIX 6

VOTING IN SINGLE MEMBER CONSTITUENCIES

                  AND THIRD PARTIES

It is widely recognized on both empirical and theoretical
grounds that our system of plurality voting in single-winner
elections is the major reason why countries like the United
States which use that system wind up with two party
dominance.  Plurality voting in which a voter can cast only
one vote and the person who gets the most votes, not
necessarily a majority, wins leads to vote splitting, the
spoiler role, and the wasted vote which compel groups
and voters to coalesce around and vote for one of two
major parties.

In principle it would seem that a system like approval
voting, in which voters can give one vote each to the
candidate or candidates they support with the candidate
having the most votes winning, would break with this
pattern and open up the political process to third parties.
This would be because approval voting reduces the
necessity of vote splitting and gets rid of the wasted
vote.  But clearly, this would not be sufficient to open up
our political processes to third parties as illustrated by
a situation in which under approval voting third parties
had around a 20% support level with the two major
parties having around a 40% support level each.

But even in this type of situation in elections with three
or more candidates for single member constituencies
a compelling case can surely be made that approval
voting would be a clearly superior system to either
plurality voting or instant runoff voting.

The case of instant runoff voting can easily be disposed
of in that one can make a compelling case in a macro
or aggregate sense that instant runoff voting, IRV, is
even a worse system than plurality voting.  As the
empirical evidence and simulations show, there is a
marked tendency for IRV to give for single-member
constituency elections results very similar to those of
plurality voting with one notable exception: its violation
of the monotonicity principle.  That is, under IRV it is
possible for a candidate to lose an election solely due
to getting more support in the course of a campaign or
for a candidate to win solely due to losing support!
Proponents of IRV argue that these are rare cases,
perhaps once in a century.  Unfortunately, the evidence
does not support that contention.  In fact the evidence
indicates that the closer a multicandidate election or
the more candidates this problem can arise with
disturbing frequencies.

Simulations by Ka-Ping Yee as related by William
Poundstone in his piece on "A Test Drive of Voting
Methods" on the Internet indicate that approval voting
gets results that are more similar to those under a
Condorcet or a Borda election than do either plurality
voting or IRV.  That is, approval voting has a strong
tendency to elect the candidate who would win in all
the pair-wise (one-to-one) contests possible from the
field of candidates--the Condorcet winner.  Or, in the
event there is not a Condorcet winner or approval voting
selects a winner other than the Condorcet candidate,
it comes close to selecting the candidate who in all
the pair-wise contests possible from the field of
candidates would get the most votes--the Borda
winner.  Given the vulnerability of a real world Borda
elections to tactical voting, it may be that an approval
voting outcome may come closer, given voters'
preferences, to the results of a "sincere" Borda count
than an actual Borda election.

In short, an approval voting election has a tendency in
a multicandidate single member constituency to elect
the candidate who is most generally popular or at least
the most acceptable to the electorate.  These, of course,
are descriptions which one can apply to the Condorcet
or Borda candidates who Sir Michael Dummet argues in
his book "Principles of Electoral Reform" (Oxford University
Press, 1997) are the candidates most representative of
their electorate in single-winner elections.

Approval voting has three advantages over either a
Condorcet election or a Borda election both of which
require voters to rank candidates in order of preference in
the voting process.  First, approval voting is a more
transparent system in terms of voters being able to
understand how the results are arrived at than are ranking
systems.  Second, related to this, feedback for tactical
voting, given the constraints of other voters' preferences,
is also likely to be more transparent with approval voting.
And thirdly approval voting does not suffer from something
like the Condorcet paradox in which a winner cannot be
determined nor is it subject to the kind of dysfunctional
tactical voting that can infest a Borda election.

Given the above considerations, it surely is clear in
multicandidate elections that approval voting can give
different results from a plurality election outcome in
single-winner elections. 

Surely in the 2000 Florida presidential election had
approval voting been in place Gore would have likely
won since, given their preferences and Nader's realistic
chances many of his supporters would have had an
incentive to cast an additional vote for Gore.

In the 2006 Minnesota Governor's election the
Independence Party ran a candidate who was well
known state wide and who by all accounts performed
much better in the debates, but could garner only under
seven per cent of the votes.  But had such an election
been held under approval voting, one could not exclude
such a candidate winning given the absence of the
wasted vote under that system.

Because of the  realities of vote splitting, particularly
in Quebec, during the May 2011 Canadian Parliamentary
election, the outcome gave a disproportional number of
seats to the Conservatives at the expense of the Liberals.
Surely had approval voting been in place at the time, both
Liberal and New Democratic Party candidates in Quebec
would have fared much better since there need not have
been wide spread vote splitting between the more
representative candidates on the majority liberal spectrum
of the electorate in that province.

In light of these three examples, it ought to be obvious
that if you had a roughly even split between three or more
parties with the normal variances in closely contested
elections, one would expect to have much more
proportional results in seats won under approval voting than
under plurality voting.  Given this and our earlier example
of a situation in which third party support was half that
of the two major parties in an approval voting election, it
should be clear that whether approval voting opens up
the political process to third parties or not depends on
circumstances that may or may not be present.  It is
this issue that supporters of approval voting and
strategists for third parties need to focus on in advocating
and dealing with that system.