Choosing a new Selectman

Tuesday night we chose a new member of our Board of Selectmen from the three candidates who put their names in.  Since we had a strong suspicion that we were not going to agree, my fellow Selectman Scott proposed that we make our decision by using a ranking system.  We each took the three candidates and ranked them first choice, second choice, third choice, using numbers, 1, 2 and 3.  Then we combined the ranks for each candidate, and because 1 was the highest, we took the person with the lowest score.  Not the one I would have chosen, but as I have said, the choices were not what I might have wished.  We do have a new member of the board so that there will be no tie votes.  He has come in to Town Hall and met with the Town Administrator to learn about the job, which is an excellent sign.  And there is an election in March.

Comments

[JS Narins]

Fantastic!

You used what is commonly called the Borda voting system, which very well if the votes are public and the number of voters is small.

The college football coaches who get to vote on the top 20 teams nationwide use Borda.

Let's say the coach of OSU knows he is in #1 or #2, and Nebraska is the top competition. Using Borda, the OSU Coach could say that Nebraska was #20, even though he knows it was #1 or #2 at worst.

Since the coaches votes are made public, and the total pool is fairly small, the coaches are forced to vote honestly.

Voting is a subset of what is called Game Theory in mathematics. It's also sometimes called "Social Choice Theory." It has been proved that there is no perfect voting system (Nobel Prize winning economist Kenneth Arrow proved it in 1956) but that there are good and bad systems.

The best system is based on the work of the Marquis de Condorcet, a personal friend of Thomas Jefferson. He didn't finish in time for America, however.

Greens and Libertarians promote something called "Instant Runoff Voting" which is, by comparison, as stupid as dirt.

:)

[bloomingpol]

My husband says I got conned by my fellow Selectman. But it was that, or a stand off. Maybe I should have held my ground and asked for a new batch of candidates.

[JS Narins]

Well, no voting system will work if the candidates are rotten, but Borda often can work in those situations.

The better way, Condorcet, (a french name, so pronounced like Chevrolet), involves putting the results in a matrix. So, the ballots are the same, but the counting is harder.

Plus, you need to agree on a tiebreaking system in the first place.

There are a few web resources on voting, but they aren't written particularly well...

One guy[1] is totally convinced that his variation of Condorcet is the best. He might be right. I know one large group that uses it for their elections.

A nice guy[2] has a site on all voting methods, but with obvious favortism towards Condorcet. It's more informative, and lists _many_ alternative voting systems, but does so in a confusing way.

And then there is the Election-Methods mailing list. Lots of math talk here, but there are also weird bits of information floating about, especially about who is using what voting system and where. This is the home page[3] for the mailing list, and, honestly, this page is probably the best now. I was on the list before they had this page.

The voting system doesn't sound like a scam, as long as the votes were made public.

[1] - http://www.ElectionMethods.org
[2] - http://www.Condorcet.org
[3] - http://electorama.com/em

[JS Narins]

Oh, the way to "rig" a Borda election seems to be to run multiple candidates who are identical. They are commonly called clones. I am not a borda expert.

"Consider an election with three candidates. Eric is right-wing and Fran and Gary are left-wing. 63% of the voters are right-wing, 37% are left-wing and all of the voters prefer Fran to Gary because of a scandal involving Gary, so the sincere votes are
63:Eric>Fran>Gary
37:Fran>Gary>Eric

Borda gives the win to Fran even though Eric received a strong majority of first-place votes and would have won handily if Gary hadn’t run, showing that parties have incentive to saturate an election with their candidates under Borda. Fran and Gary are called clones in this election because they’re next to each other on every ballot. Clone-independent methods give the same results if a group of clones is replaced by one candidate; any reasonable clone-independent method would choose Eric in this election, removing the candidate-saturation incentive. "