Election Theory

In the USA we customarily use “plurality voting” to choose elected officials. This methodology’s chief advantage is its simplicity: each voter casts a single vote for a single candidate, and after the numbers are totaled the candidate with the most votes wins. It’s a system that is easy to administer and for the voters to grasp: “designed by geniuses to be run by idiots” as the saying goes.

But the 2000 presidential election exposed a rather severe problem with this simple system. Mr. Nader’s “stolen” votes are commonly believed to have been behind Mr. Gore’s loss, in that those voters would likely have preferred Mr. Gore over Mr. Bush. This splitting of the vote is known as the “spoiler effect” and is often cited as plurality’s chief flaw.

A common fallacy is to think that plurality voting is the only — or even best — election methodology. Voting theory emerged as a legitimate field of academics before the French Revolution, so after over two hundred years of study the science can be regarded as mature.

A World of Imperfect Alternatives

Instant-Runoff Voting (or IRV for short) is used, among other places, to elect Australia’s House of Representatives and Ireland’s President. In IRV, voters rank the choices in order of preference; the last-place choice is removed from the ballot, their votes reassigned to the remaining candidates; the cycle repeats until there is a clear majority winner. Though this methodology is well-liked as a general alternative to plurality voting, it brings its own flaws to bear. It is more complex than “vote for your first choice” and it has a paradoxical behavior called ‘violating monotonicity,’ whereby voting for your favorite candidate can actually cause him to lose.

The Borda Count is less well known and less well used at a national level. Voters rank candidates by preference; candidates are assigned points according to their position on each voter’s ballot — say, 2 points for first place, 1 point for second, and 0 points for third. Points are tallied and the winner is the candidate with the most points. This methodology’s major flaw is that it can easily result in a minority candidate winning the election. On the other hand, due to the point system, the winning candidate usually has solid appeal across many voters. In this way, a Borda Count election is called “consensus voting” rather than “majoritarian” because it can result in a winner with broad general appeal rather than the first choice winner.

It Gets Even More Complicated

Voting Theory is a bona fide science. It incorporates aspects of social science, mathematics, political science, and even economics — all these are employed to understand the ramifications of election methodologies. Criticisms of each methodology are deep and emotional, and range from mathematically-backed analyses to discussions of disenfranchising (or over-indulging) minority voters.

There are numerous criteria that have emerged to help define the effectiveness and flaws of voting methodologies, and every voting system violates at least one (and often several) of these criteria:

  • ‘Monotonicity’ evaluates the paradoxical behavior that additional votes for a candidate can actually harm that candidate.
  • ‘Consistency’ evaluates whether an electorate arbitrarily divided would have the same outcome as the total electorate.
  • ‘Participation’ examines another paradoxical behavior in which not voting can actually help one’s preferred candidate win.
  • ‘IIA’, or Independence of Irrelevant Alternatives, goes deep into human psychology and irrationality and states that the addition of a third option C should not invert an existing preference of A over B.
  • ‘Reversal symmetry’ concerns inverting all voters’ preferences, noting that the original winner A must no longer win.

For deeper analysis of these and other aspects of voting theory I recommend you begin here.

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