Reader F. Tyler asks the following (slightly edited) question regarding the Borda count, a voting method in which people rank alternatives, higher-ranked alternatives get fewer points, and the option with the fewest points wins, just like golf (see this post and its follow-up on basic problems with voting):
"But isn't there a problem with the Borda count assuming that these preferences are of ratio interval, when they are, in fact, simply ordinal? If I'm voting for Perot in 1992, I'd MUCH prefer Bush, and HATE to see Clinton elected. Similarly, in 2000 I cast my vote for Nader, and would be ok with Gore, but Bush Jr is the worst. Right?
There isn't a consistent ratio presented. Maybe if I gave Nader a 1, Gore a 3 and Bush a 10, it would reflect my preferences, but the Borda count doesn't seem to allow that."
F. Tyler is absolutely right. First, a little background. Economists (of the academic variety) sometimes think of preferences as ordinal, i.e., they are just a ranking and nothing else. But preferences may also be cardinal, i.e., they reflect how much you prefer one option over another. Although Borda argued his method as capturing some of the latter, voters still just rank alternatives, meaning their preferences are treated as ordinal.
There are methods of voting that attempt to capture cardinal preferences, or utilities. For example, in one method, each voter has a certain number of points she can distribute among candidates. In Tyler's (2000) example, if he had 100 points, he could give Nader 70 points, Gore 23, and Bush 7, roughly reflecting the strength of his preferences (assuming his Borda-like scheme above translated into liking Nader three times as much as Gore and ten times as much as Bush).
However, even this method is problematic because of so-called interpersonal utility comparisons. The problem is, there isn't any obvious way to compare how strongly one person feels about something to another person's feelings. People try—there are those who erroneously believe you can do it by asking people how much they would pay for a certain choice over another, problematic because, despite what misguided Chicago-school acolytes and stock brokers will tell you, not everyone cares about money equally—but really, nobody knows a theoretically sound way to do it.
An interesting question is whether such a method would be susceptible to Arrow's Theorem problems, as other methods are. My guess is that it would be, but I don't have my textbooks in front of me and don't recall the answer perfectly. As always, stay tuned. In the not-too-distant future, I'll talk about arguments for and against voting rules such as the Borda count.