Friday, March 24, 2017

Why we love the Borda count

"My scheme is intended only for honest men."
The Borda count is a great voting system that doesn't get enough attention. It is really easy to understand and is very useful for certain types of elections. It does, however, have a serious flaw that you need to be aware of before using it. More on that later.

A quick bit of history. The man credited with inventing the Borda count is Jean-Charles de Borda. He invented a lot of things and has a crater on the moon named after him.

How the Borda count works

The Borda count is really simple. Suppose 5 candidates are running in the election. The voters rank the candidates, and each candidate gets 4 points for every first choice, 3 points for every second choice, 2 points for every third choice, 1 point for every fourth choice, and no points for last choices. You count up the points, and the person with the most points wins.

Sometimes you will see other point systems. E.g., 5 points for a first choice and 1 point for a last choice. Sometimes it is reversed and you get 1 point for a first choice, 5 points for a last choice vote, and the person with the fewest points wins. You get the same winner either way so it doesn't matter.

When to use the Borda count

The Borda count is especially useful when:
  1. there are a large number of candidates,
  2. the number of voters is relatively small compared to the number of candidates, or
  3. you need to rank all of the candidates instead of just picking a winner.
One good use of the Borda count is setting an agenda for a meeting. Suppose that 20 people are voting to rank 30 agenda items, and it is desired to get an ordered list of agenda items to address at the meeting. Using instant runoff voting for this kind of election might result in a lot of ties and not produce a satisfactory rank ordering of all the agenda items (because many agenda item may get the same number of votes). With the Borda count, however, each first choice gets 30 points, each second choice gets 29 votes and so forth. With 20 voters, ties are unlikely, and you will get a nice clear ordering of agenda items.

Although most people haven't heard of the Borda count, it is used for some very well known elections. The Borda count is used toe elect the MLB Most Valuable Player award, the Heisman trophy, and the winner of the Eurovision Song Contest.

What is this flaw?

The Borda count requires that voters vote honestly, and voters can manipulate the results by voting dishonestly. Monsiuer de Borda is famous for having said "My scheme is intended only for honest men." We'll use an example to explain what it means to vote dishonestly...

Suppose that five candidates are running for President, and that candidates A and B are easily the two front runners and they are virtually tied. Candidates C, D, and E are also running but they all are have very low support.

A voter's honest choice may be the candidate A is her favorite and candidate B is her second favorite. This voter may be tempted, however, to rank candidate B last. This way, candidate B gets 1 point instead of 4 points and candidate A has a better chance of winning.

Now imagine that all of candidate A's supporters rank candidate B last, and all of candidate B's supporters rank candidate A last. A likely result is that both of them lose and instead candidate C wins who no one really liked anyway!

For this reason, the Borda count should only be used where the voters will likely vote honestly. When electing officers of an organization, the Borda count may not be a good choice (depends on your voters), but the Borda count may be a great choice for setting the agenda of your next meeting or casual decision making like selecting a restaurant for a group outing.

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