Properties of Voting Systems
Just as there are many different forms of democracy, there are many voting
systems. In some states, you vote for a party instead of voting for individual
candidates. In others, such as Australia, voters produce a rank ordered list
of candidates according to their preferences. All systems, however, are designed
to solve the same problem of converting aggragated voter preferences to a
functional government.
A common problem with voting systems is their disincentivization of indicating
true preferences for many voters. For example, in the United States, those with
political philosophies outside the two party system often express a fear of
‘throwing your vote away’ by voting for a party which matches their preferences,
instead opting to choose Republican or Democrat depending on which they see as
the ‘lesser of two evils’. The reason they do this is that they see little
chance for their more marginal preferences to win the winner-take-all election,
instead opting to influence the outcome.
What, then, is the most fair voting system? This conversation can be informed by
a discussion of Arrow’s impossibility theorem. This theorem states that no
rank-order voting system can exist for which the following statements are all
true:
If every voter prefers A to B, then A is preferred to B by the electorate
If every voter’s relative ranking of A and B is unchanged, then
the electorate’s relative ranking of A and B is unchanged
There is no ‘dictator’, ie: a single voter who can dictate the outcome
I won’t give a proof here, but if you are interested, one can be found at
http://cowles.econ.yale.edu/~gean/art/p1116.pdf.
Arrow won the Nobel prize in economics for his work. However, some scholars
suggest that it should have gone to Gibbard and Sattherwaite for their theorem:
For all deterministic voting systems which has voters submit an ordered list
of candidates, one of the following must hold:
The system is dictatorial
There is some candidate who can never win
The rule is susceptible to tactical voting.
So the problem designers of voting systems are faced with is one of balancing
the first two Arrow properties. However, Arrows impossibility theorem does not apply
in all cases. Arrow’s theorem applies to all ordinal voting systems, those which
require voters to submit a rank-ordered list of candidates. Cardinal voting
systems, on the other hand, require voters to give each candidate a grade
independent of the grade given to other candidates. Examples of cardinal voting
systems include range voting as the classic example; in range voting, each
candidate is rated by each voter. The ratings are summed, and the candidate with
the highest rating is the winner.
This system has some very nice properties, which are expounded upon very
richly at (4). It seems from this survey that range voting is a good way
to avoid the irrationality inherent in ordinal voting systems.
(1) http://cowles.econ.yale.edu/~gean/art/p1116.pdf
(2) http://www.sjsu.edu/faculty/watkins/arrow.htm
(3) http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1116545
(4) http://www.pnas.org/content/104/21/8720.full