I recently noted that political scientists tend to argue that democracy is impossible without political parties, and expressed my doubt about the empirical truth of that statement. As a follow-up, here’s one theoretical problem with democracy, Condorcet’s Paradox, and an explanation of how parties help resolve it. In the spirit of full disclosure, while I studied the type of positive political theory discussed here, I never studied parties and elections, so I’m not actually certain that this is in fact what most political scientists think of when they talk about parties being necessary for democracy. But I won’t let that stop me, because the paradox itself is pretty cool.
Imagine three friends trying to decide what kind of joint entertainment they’re going to engage in. One wants to go to (A) a football game, would settle for going to (B) the park, but really prefers not to go to (C) the museum. Another prefers going to (B) the park, would accept going to (C) the museum, but hates (A) football. The third loves (C) the museum, likes (A) football, and loathes (B) the park. To make this clear, we can list their preference orders in a simple grid.
|Friend 1||Friend 2||Friend 2|
Naively, the friends decide to vote on what to do, and end up with a three way tie. So they try again, and pit each alternative against each other alternative, first A-B, then B-C, then C-A. But as it turns out, A beats B 2-1, B beats C 2-1, and C beats A 2-1. There is no clear winner.
This is crucially important because it reveals the important distinction between an individual and a group. An individual can have a coherent, transitive, preference order. You learned about transitivity in elementary school, but may have forgotten if you’re not a math person. It simply means that if A > B, and B > C, then A > C. Or in other words, if I like pizza more than hamburgers, and hamburgers more than hot dogs, I should like pizza more than hot dogs. Imagine the poor person with an intransitive preference order. He’d starve to death while thinking to himself, “Pizza’s better than hamburgers, I should get a pizza. But hot dogs are better than pizza, so I should get a hot dog. But hamburgers are better than hot dogs, so I should get a hot dog. But pizza’s better than hamburgers, so I should get a pizza.” It’s impossible to engage in rational decision-making if you have an intransitive preference order (the best thing to do then is select randomly). We would, rightly, say this person has a serious problem.
So individuals are assumed to have
intransitive* preference orders, but as the example shows, that doesn’t necessarily mean that a group has a transitive preference order. Our three friends are stuck mumbling, “football beats the park, which beats the museum, which beats football, which beats the park, which beats the museum, which beats football….” Their best option is to choose by playing rock, paper, scissors–i.e., randomly. We call that round-and-round problem “cycling.”
This is bad news for democracy, because democracy is supposed to tell us what the public’s preference is. We always hear the talking heads pompously proclaim, “the public has chosen…” and every politician tries to tell us “the public wants X.” But what this shows is that we can’t say that the public has a true preference order–the public’s preference order is not necessarily transitive, so we can’t say that it has a top choice. What it selected could be just a matter of which two alternatives happened to be placed before it. It was given a choice of football and the park, so it chose football, but if it was given a choice of the park and the museum it would have chosen the park, and if ti was given a choice of the museum and football, it would have chosen the museum. The public’s electoral choice could cycle, and our policy outcomes could mutate endlessly.
So how realistic is this? After all, the grid above reveals a carefully stylized model, and perhaps in real life nobody really likes the museum. Here’s the bad news. That’s the simplest model of cycling possible, 3 people with 3 options, and the larger either of the numbers becomes, the greater the potential for cycling. (One reason I’m not a big fan of very multi-party systems–think Italy post WWII.) In a large public with a large number of choices, cycling is probably an inevitable outcome, making democratic politics wholly irrational.
This is where parties come in. By proposing certain policies and pushing others off the agenda, parties help eliminate–or at least mitigate–cycling. This agenda-setting function is hugely important. If you know what the alternatives are, and know what other people’s preferences are, you can sometimes get to your own preferred outcome by manipulating the agenda.
In our example above, let’s say Friend 1 is cleverer than the other two. He proposes that they pit two options against each other, then pit the winner against the third. Hey, that sounds fair! So Friend 1, the football fan, proposes that first they vote between options B (the park) and C (the museum), with the winner facing off against A (football). He knows the park will beat the museum, and he know his preference, football, will beat the park. He has manipulated the agenda to resolve the cycling problem, in favor of his own preference. What seemed, on the surface, to be fair, may not have been fair at all. It’s certainly not what we think we want from democracy. But that’s what makes democracy actually functional.
In my next post on this subject, discussing Arrow’s Impossibility Theorem, I’ll show why your intuition that this solution isn’t quite right is correct. It violates one of the basic principles of democracy. But disturbingly, democracy can’t fulfill its own basic principles while successfully aggregating preferences into a group preference. We’ll save that one for next week, though.
* Post-hoc correction.