Thursday, November 20, 2014

Tofu Anyone? Hubris, Architecture, and Voting

I've seen law professors take on all kinds of tasks better left to others. Among those was how to design a law building. Another is how to decide what to serve at lunch. For example, on the lunch issue suppose there are 60 people with all kinds of preferences and 60 different food choices. Would it make sense to have each person vote for 5 choices and then serve the 5 top vote getters?  People who know about cycling, preferences, and rigging know this will likely tell you very little about what preferences really are. First though Rather than 60, let's say there are 3 choices and 3 people. The choices are roast beef, chicken, and soup.

Person one ranks them like this: roast beef>chicken>soup
Person two: chicken >soup>roast beef
Person three: soup>roast beef> chicken.

If everyone gets one vote, it is a three way tie. So how do you rig this to get where you want to go if you personally favor roast beef. First you ask a vote who wins between chicken and soup. The answer is chicken. Now who wins between roast beef and chicken. The answer is roast beef. Having the power to determine how the vote is to be conducted gives the "authority" to determine the outcome.

How else can being the "authority" who determines how people are polled dictate outcomes? Let's say there are 7 choices for lunch and 10 people voting and they each get to vote for (but not rank) their top two. That's 20 votes in total and it comes out like this:

Roast beef - 4
Tofu (gads!) -4
chicken -3
tuna -3
beanie weenie -3
cheese -2
PB&J -1

Clearly the faculty prefers Roast beef and tofu. Right? Just hold on a bit. Actually 60% prefer anything other than tofu and 60%  are saying "Please God anything but roast beef, it made us really sick the last time we had it."  If you knock out cheese, beanie weenie, and PB&J and revote, roast beef and tofu may well fall off the list completely.  In fact, if you do not do that, those voters are, in an sense, disenfranchised and you really do not know much at all about preferences.  This is all a middle school level of understanding and why even in places like Louisiana there are run offs.

So what would be the rationale for not having a run off? I  can think of three: 1) you do not care what people want, 2) you do not understand how imprecise one ballot can be in gauging preferences when there are many votes and many choices, or 3) you have a hunch you can deliver 4 roast beef votes but no more and you are worried about the outcome of a second ballot. In the case of law professors, it could be any three.


Anonymous said...

Runoffs don't help these problems. Arrow's theorem and its consequences apply to an incredibly broad range of aggregation methods.

Jeffrey Harrison said...

That is why the second example is not arrow's impossibility theorem.