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By Jay Cost

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The Poll I Would Like To See

One of the problems with media polling in the primary campaign is that it uses the same format as in the general campaign. That is, all of the candidates are set against one another, and the respondents are asked to select only their first choices. The "winner" of the poll is the one who has the most people register him or her as their first choices.

This type of polling is efficient for the general election because that is essentially what happens on that fabled Tuesday in November. We vote for our first choices, and our first choices only. Whoever is the first choice of the most people is the winner. Thus, the poll is an efficient way to gauge public opinion in advance of the election. The poll and the election are so similar.

However, in the primary season, this type of polling becomes inefficient. This is because most voters do not get to make the choice in the voting booth that respondents make in a poll. Primary voting is staggered. Some of us vote after others. This is important because candidates drop out. In reality, Iowans are the only people who make a selection for the presidential nomination the way respondents answer polls. The rest of us have to choose from a smaller field. So, this format of polling does not capture the reality of the primary election.

Well, Jay, you might say - that may be true. But aren't you just being unnecessarily technical here? After all, just how problematic could this possibly be? Maybe it is the case that the polls do not give us an absolute sense of the race, but they at least give us a relative sense of the race. We know who is beating whom, even if we do not know by how much. For instance, if Clinton is ahead of Obama in the polls - we know that, as a whole, the electorate prefers her to him, regardless of who else is running. So, at least we have some "purchase" on the state of the race.

Not true!

This argument runs afoul of the fallacy of composition. I would certainly agree that every individual has what might be called a rational "preference ordering." That is, every individual could arrange his or her choice for the Democratic nomination in a way like the following:

Clinton > Obama > Gore > Edwards


Gore > Obama > Edwards > Clinton

For either of these individuals, if you eliminate Edwards from the contest, you are not going to change how either person feels about Clinton in relation to Obama. You would still see:

Clinton > Obama > Gore


Gore > Obama > Clinton

This is called the "indepndence of irrelevant alternatives." Your preference about Edwards has no bearing upon whether you prefer Clinton over Obama, or Obama over Clinton. This is part and parcel of basic human rationality. We expect every mentally sound person to exhibit this kind of behavior. At Thanksgiving dinner, you would expect your aunt to prefer mashed potatoes over scalloped potatoes regardless of what else is served. If she changes her preference between the two of them because you serve asparagus instead of peas - you will start to worry about her!

On the other hand, it is often the case that, as a society, we collectively fail to exhibit this "rationality." That is, when we aggregate the preferences of everybody together, we can sometimes wind up with a result where the presence or absence of peas changes our mind about the better potato.

The following is a good example. Suppose that the Democratic primary electorate is composed of four people who exhibit the following preference ordering:

Voter 1: Clinton > Obama > Edwards > Gore

Voter 2: Edwards > Obama > Clinton > Gore

Voter 3: Obama > Clinton > Gore > Edwards

Voter 4: Clinton > Edwards > Obama > Gore

Let us suppose that, to determine what the group prefers, we give each candidate a score between 1 and 4 depending upon where they end up with each voter. Whoever has the highest score is the group's preferred choice. In this case, Clinton would get 13. Obama would get 12. Edwards would get 10. Gore would get 5. Thus, we could say that the group prefers:

Group: Clinton > Obama > Edwards > Gore

And, in an election, Clinton would win with 50% of the vote.

But what if Edwards were to drop out? We would see the following preferences from our four voters:

Voter 1: Clinton > Obama > Gore

Voter 2: Obama > Clinton > Gore

Voter 3: Obama > Clinton > Gore

Voter 4: Clinton > Obama > Gore

If we reassign scores for each candidate between 1 and 3 depending upon where they end up for each voter, we get: Clinton with 10, Obama with 10, Gore with 4. Thus, the group would then prefer:

Group: Clinton = Obama > Gore

And, in an election, there would be a tie between Obama and Clinton.

See the "irrationality" here? In the four-way race, the group as a whole preferred Clinton to Obama. If the group was acting "rationally," Edwards's exit from the race should have no effect on how the group views Clinton in relation to Obama. And yet, it did! An "irrelevant alternative" was eliminated, and yet the relationship between Clinton and Obama was not "independent" of the elimination.

This is an example of a general problem with all voting systems. Regardless of how you design a social choice mechanism - be it winner-take-all, two-stage voting, open primary voting, whatever - you can always arrange the preferences of the voters in such a way that you can wind up with an "irrational" result such as this.

Of course, these "irrationalities" are not actually irrationalities. Rationality is something the characterizes a person. It is a fallacy of composition to think that just because a person can be characterized as rational or irrational, a group of persons can be, too. A group is neither rational or irrational.

This is important. If we say that a group is irrational, it might be that we cannot predict its behavior. But we are not saying that; all we are saying is that rationality/irrationality is not a dichotomy that applies to groups. So it is indeed possible to predict group behavior. If we know what everybody's preferences are, and we know the voting system, and we know the changes in the race, we could predict what would happen, just as we could predict that - in the above example - Obama would tie Clinton if Edwards were to leave.

Unfortunately for us, we know the voting system, we know the changes in the race, but we do not know everybody's preference orderings. Why? Because media polls do not tell us.

I'll wager not only that candidate-sponsored polls ask voters to rank the candidates in the above manner, but also that some candidates have strategies to knock out other candidates. It seems intuitive - to me, anyway - that if Edwards were indeed to exit the race, Obama would be aided. I am guessing that the people who place Edwards above Clinton also place Obama above Clinton. Just a hunch. So, Obama has an incentive to knock Edwards down, Clinton has an incentive to prop him up.

My intuition is that there is something similar going on with the Republicans, too. Giuliani is in the lead right now, but it seems to me that this might not hold if candidates start exiting the race. In other words, like Clinton, he has an interest in keeping the field as large as possible. Others, namely McCain and Romney, might have an incentive to attack one another if they suspect they would win in a smaller field.

If it were the case that everybody voted at the same time, the media's polling method would be ideal. But that is not the way it is. So, the poll I would like to see is a query of primary voters that asks them to rank the candidates from worst to first, and let us view the raw data. Maybe then we could get a sense of what will happen.

One final point. This phenomenon works just the same when you add an alternative as when you subtract one. When we ask, "Fred Thompson is in, whom does he hurt?" we are implicitly acknowledging this point. Even though the presence or absence of Fred Thompson has no effect on whether an individual prefers Giuliani to McCain, it might be the case that it changes how a group relates Giuliani to McCain.

Yep - primary polling is inefficient. No doubt about it. It would be nice if it were altered to better reflect the reality of the primary voting season.

-Jay Cost