AC and Voting

     Living with roommates means there are certain things you have to agree upon so you can live amicably. One of those things is how high/low you set the AC. The way we determine the AC is by simple majority with runoff. We first determine what we deem as a cold temperature, a moderate temperature, and so on until we have 4 options (cold, warm, moderate, or the AC is off and windows are open). For us, we need 3 out of the 5 of us to agree upon a temperature for it to pass. Cold passes under a simple majority after a runoff. However, upon reviewing the different types of voting methods that we learned in class, I wondered if Borda would produce a different result. Borda picks the Condorcet winner more often than simple majority with runoff so I thought that the Borda method might be a better (where better here simply means: picks the Condorcet winner more often) method for determining the AC than the simple majority with runoff.

To demonstrate why the Borda method might be better I laid out my friends' preferences in the following table:

	Sam	Nathan	Zachary	Sami	Alex
4	cold	warm	Off	cold	off
3	off	cold	moderate	off	moderate
2	moderate	off	warm	moderate	cold
1	warm	moderate	cold	warm	warm

Cold= 4(C) + 4(C) +3(C)+2(C) +1(C) =14

Off= 4(O)+4 (O) + 3(O) + 3 (O) + 2(O) + = 16

Moderate= 3(M)+3(M) + 2(M) +2 (M) + 1(M) =11

Warm=  4(W) +2(W) + 1 (M) + 1 (M) +1 (M) = 9

In a simple majority after a runoff “Cold” wins. But with the Borda method “off” wins. However, in a pairwise election where it is “Cold vs Off’, “Cold” wins. In this situation it seems that the Condorcet winner is “Cold” yet Borda chooses “Off”. In this unique example simple majority with runoff chooses the Condorcet winner yet Borda does not, even though Borda on average chooses the Condorcet winner more than the simple majority with runoff.