Voting on Dinner

The Voting Game

You are at work and your boss presents 3 options for a team dinner: Taiwanese, Indian, Mexican. There are 10 people on the team, you can preferentially rank which place you want to go. The first choice that you pick has 2 points, the second has 1 point, and the last gets no points. The restaurant with the most total points after all the rankings are tallied will one. Suppose you have the following voting profiles:

4 people have : Taiwanese > Indian > Mexican 4 people have : Indian > Mexican > Taiwanese 2 people have : Indian > Mexican > Taiwanese 2 people have : Taiwanese > Mexican > Indian

The result would be:

Indian: (6 * 2) + (4 * 1) = 16 Taiwanese: (6 * 2) = 12 Mexican: ( 6 * 1) = 6

Win?

The above voting algorithm is referred to as the Borda Count. Does it same fair? The aspects that make it seem fair are the following:

1. Every outcome has a chance of winning
2. There are no "dictators", i.e a single player in the voting system who has complete control over the outcome

However, in the language of social choice theory, researchers have decided that there is actually something imperfect going on here. It is because, since I really care about Taiwanese food, I could convince all of the 4 people who have the profile Taiwanese > Indian > Mexican to switch to Taiwanese > Mexican > Indian.

This bumps Indian's score down to 12, and Mexican's score up to 10. Now, instead of having Indian being a clear winner, we have a toss-up and I have increased my own likelihood for eating Taiwanese food. This, could be viewed as potentially a bad thing for democracy since we have voters who are not honestly expressing their preferences in order to get a more preferred outcome. In most voting systems, we won't see other people's votes, and we also won't be able to change our votes once they are cast.

However, in the context of a normal preferentially ranked ballot, it is certainly the case that every person will have their own internal "true" ranking. It is also true that we likely will have some rough estimate of what we think the distribution of total overall votes will be by other people. From these two facts, we may also misrepresent our preferences to achieve our results.

Random Reflections

When I first read about strategic or tactical voting, I too agreed with the literature that this "felt" unfair. Thinking about it later, I wasn't so sure. Voting too is a game, and in almost any multi-player game it is natural, and indeed sometimes favorable for players to try to maximize their own utility. To counter my own counter-argument though, there are at least two straightforward reasons why we would still want to avoid voting algorithms that are susceptible to such tactics:

1. Some players are more willing to "play" the game than others - giving them an unfair advantage over outcomes. In a real-life context, this could often just be people who are more knowledgeable, or more educated -> and this could lead to a self-reinforcing loop of the sorts of people who are in power
2. Even if every person were aware of this fact, and acted in an optimal way in terms of maximizing their own utility, it is also a well-known fact that this may lead, in game theory, to waht is called a Pareto Dominated Outcome. As in, it is a Nash Equilibrium for all the players (they cannot change their profile for a better outcome) but it leads to an overall outcome that is dominated by another outcome (by being worse in utility for every possible player)