[This is the sixth essay on the major contenders for the presidential nominations. See the earlier ones on Clinton, Edwards, Obama, McCain (Parts 1 and 2) - and my introduction to the series.]

When Rudy Giuliani declared himself a candidate for the Republican nomination, many pundits were skeptical. I think that, deep down, many of them remain skeptical. They have backed off their predictions because Giuliani has been able to hold a lead - though, of course, the lead has diminished. However, I think that most of them have ceded the nomination question simply because the data is forcing them to do so - not because they have found any intuitively compelling reasons.

My intention here is to offer such a reason - which is not to say that this essay amounts to a prediction that Giuliani will win the nomination. I am going to offer a model, i.e. a simplified version of reality, whose purpose is to demonstrate my point that Giuliani is genuinely competitive, not that he will necessarily win.

In my essay last week on John McCain, I argued that several pundits had misunderstood his decline because they were working from a naïve understanding of the median voter theorem. The theorem predicts that a candidate can win an election by adopting the issue position of the median voter; however, it also makes a number of assumptions to arrive at that prediction. One such assumption is that there are only two candidates in the race. When we alter that assumption, we allow for the possibility that a moderate Republican might win the nomination not having secured the median Republican voter - i.e. a conservative. This is how a seeming moderate, like McCain, might nevertheless win the nomination.

I think that most pundits are rejecting, or at least were rejecting, the viability of the Giuliani candidacy based upon a similarly naïve view of the median voter theorem. I think that they have in their minds a notion that to win the Republican nomination, you mast tack to the median voter, something that Giuliani simply cannot do. He is a social liberal, after all. And social liberals do not win the GOP nomination.

I think this use of the median voter theorem is naïve. The problem for its application to Giuliani is not just that the number of candidates nullifies the equilibrium position - though this is surely a problem in using the model to predict Giuliani's fate. Like McCain, a moderate like Giuliani benefits from a multi-candidate field. So, what I argued in Part 1 of my essay on McCain can also be applied to Giuliani. But the theorem has further problems when it is applied to Giuliani. The two candidate assumption is not the only problematic one; I would argue that, should the race narrow to two candidates - say, Romney v. Giuliani or Thompson v. Giuliani - Giuliani could still win.

Why? Recall from my discussion of the theorem that one of its assumptions is that there is only a single "issue dimension." What does that mean? It means, simply, that voters are voting for a candidate for a single reason. It could be a reason as broadly defined as ideology. As an example, think of the American Conservative Union's legislative score. A voter positions himself as, say, an 85 on the ACU scorecard. He then chooses the candidate who is closest to that position. In this way, his vote choice is predicated upon a single dimension.

If we assume that there is a single issue (like ideology) in a three voter election, and we accept the rest of the theorem's assumptions, the median voter theorem produces the following result:

Both candidates (in a general election like this) will flock to the median voter.

Must an election be fought along a single dimension? No. Theoretically, an election could be fought on any number of dimensions. Practically speaking, the addition or subtraction of issue dimensions from the public forum is an act of political power, one that is strategically employed to maximize the likelihood of electoral victory. A good example is the cultivation of the "personal vote" in congressional campaigns. When incumbents try to get voters to vote for them based upon personal/biographical reasons like experience, and not based upon issue positions, they are adding another dimension to the electoral contest.

To appreciate exactly what I mean here, consider a hypothetical example. You and your friends are voting on what movie to go to. This is an election based on a single dimension. However, you soon realize that there is disagreement about what restaurant to go to afterwards. So, you decide to vote on both questions at the same time - with several of your friends making proposals for restaurants and movies. Then, each of you votes upon the proposals. For instance, Robbie proposes Die Hard and Applebee's, Richard proposes Transformers and Chili's, Levon proposes Harry Potter and P.F. Chang's - and the group decides between Robbie and Richard and Levon's proposals.

Of course, you are probably thinking that it is much more efficient to distinguish the movies from the restaurants - have a separate vote on the movie and a separate one on the restaurant. But we cannot do this in a representative democracy. We do not vote for issue positions, we vote for persons who represent a cluster of issue positions. And so, elections are fought upon multiple issue dimensions.

When we factor in a second issue dimension, we lose the equilibrium position of the median voter. In other words, no longer is it the case that the candidate who adopts the median position will beat the candidate who chooses any other position. To see what I mean, consider the following example. Suppose that an election decided by three voters - A, B, and C - is fought over foreign policy and domestic policy.

The dots with the letters indicate each voter's ideal points - that is, if a given voter was in charge of selecting the "mix" of foreign and domestic policy, he would choose his ideal point. The circles around the dots indicate what we might call "indifference zones." A given voter prefers points on his circle equally - i.e. he is indifferent between them. He also prefers points within his circle to points outside his circle.

Importantly, there are no points that are equilibria like the median voter is in the single dimension. In other words, there is no place where candidates are in a "best response" to one another. This means that there is no way to predict where candidates will ultimately position themselves. Therefore, there is no way to predict who will win. [Of course, it is possible for voter preferences to be distributed in a way such that there is at least one equilibrium. However, the requirements are fairly stringent.]

This is not to say that there are not positions that benefit society more than other positions. The triangle with the dashed line represents such an efficiency zone. If a candidate takes a set of issue positions that places him within this zone - there is no way that he can alter his policy positions to satisfy the group's aggregate preferences more efficiently. Any movement within the triangle will move him closer to some voters, but at the expense of others.

In the median voter theorem, there is only one point that is efficient in this way - the median voter! So, this is what happens when we assume that an election is fought over two issues rather than one. We move from a single point to a zone of points that are efficient. The consequence is that candidates potentially have more leeway to position themselves. They can place themselves anywhere in that triangle and be efficient. Importantly, in a two-dimensional race between two candidates - simply being at the median on one of the dimensions is not sufficient for electoral victory. The other candidate might be able to split your voting coalition by making clever use of the other dimension.

This is why I would claim that Giuliani is viable - even in a two candidate contest. There is more distance between the median voter and him on the domestic ideology dimension than there is between the median voter and, say, Mitt Romney. However, Giuliani is closest to the median voter on the foreign policy dimension. This places him well within the efficiency zone of the electorate. It does not mean that he will win the nomination. But it does mean that he is a viable candidate whose policy positions are an efficient expression of the sentiments of the Republican Party.

This, then, is the basic intuition. It is why I have taken the trouble to draw up a graph with all of these symbols and what not. It is to demonstrate that, with in a race over multiple issue dimensions with two candidates, voting coalitions in one dimension may be split by the other dimension, and so tacking to the median of one dimension is not sufficient for electoral victory.

In most presidential primary contests, I would argue, you do not really have two salient issue dimensions. Republicans and Democrats usually select their nominees on a single dimension - namely, domestic ideology. Foreign policy is rarely an issue.

However, I would argue that it is an issue in this campaign. Specifically, I would argue that Republicans are looking for a candidate who can credibly warrant that he will be a competent leader in the fight against terror. Thus, theirs is an election that is being fought on two distinct dimensions. And it is on this second dimension that Giuliani appears to have a distinct advantage over his opponents. No candidate, with the possible exception of John McCain, can make warranties on the fight against terrorism as credibly as Giuliani can. No candidate maximizes the ideal point of the median Republican primary voter as well as Giuliani does. As I said, this buys him latitude in the domestic ideological dimension. This is the way that a social liberal might win the nomination of a socially conservative party.

Importantly, this is not reducible to strategic primary voters compromising their issue positions to vote for a candidate they believe will win. Giuliani voters are voting their preferences.

Does this mean that Giuliani will win the nomination? No. As I said, in a two-dimensional election, there is probably no equilibrium position. So, in theory, a candidate could take the issue position of Denny Kucinich and still win the Republican nomination (it all depends upon what the alternatives are). The point is that Giuliani is a viable candidate whose mix of foreign and domestic policy are efficient aggregations of party sentiment. Even though he is a poor match on one dimension, he is an excellent match on another.

Of course, there are problems with this model - as with any model. After all, it is a highly simplified version of reality that we have used to give us some purchase on what is going to happen. We have learned from it - but we should not tie ourselves to it slavishly because, after all, the real world is more complex than a triangle, two lines, some circles, and a few dots!

One major problem with this is that we have assumed that voters have perfect information. I mentioned last week that this is one reason why McCain is in such trouble. In reality, voters have imperfect information about him, and so are going to avoid him because he is far too risky. This could cause trouble for Giuliani as well. I made the general point last week that voters use "heuristics" - or informational shortcuts - to make decisions despite imperfect information. One such heuristic is the political party. Another heuristic would be, I'd wager, cues from elites whom voters respect. Rush Limbaugh is a great example of such a heuristic for conservative voters. It is not that people who listen to Limbaugh do not think for themselves. It is, rather, that Limbaugh is an informational elite who shares his listeners' views. Thus, if Limbaugh is opposed to a certain proposal, listeners can safely assume that, if they knew as much about the specifics as Rush knows, they would oppose it, too.

This is a function that people like Pat Robertson and James Dobson also serve. They act as informational cues to their constituents. This could be trouble for Giuliani. Many of these religious leaders seem to be opposed to Giuliani's candidacy - and this might have the effect of signaling their constituents that Giuliani is, for them, an inefficient selection. The effect of this might be to place Giuliani, in the minds of these voters, further from their ideal points than he might actually be. This, I would wager, is why Giuliani is taking such pains to certify himself on the question of judges. He is trying to signal to voters that he is not too far from their ideals on the domestic ideology dimension.

I'll close with a final question, one that - like the informational cue that Focus on the Family offers - cannot really be captured by the model I have delineated. It's just a question. I am not sure what the answer is.

How many Republicans can actually vote against Giuliani when given the chance? I mean this regardless of the purely rational calculations I outlined above. I am talking about emotions and sympathy - i.e. voting against your rational interests because of your emotional response to a particular idea or person. Rational choice theory fails to capture this in a way that is not reducible to ad hoc modifications of its basic principles. This is a major drawback to the theory because emotions run high in politics - and they can be of great use to candidates. I wonder if they will not help Giuliani.

In the minds of, minimally, conservative Republican voters - 9/11 initially produced two political heroes. George W. Bush managed the nation's response to the attack, but Rudy Giuliani managed the city's response. For a whole host of reasons, Bush's status as a hero has since been compromised - even in (I would wager) the minds of many Republican voters who continue to offer support of him to pollsters. Giuliani's status, on the other hand, has not been compromised. My intuition is that for Republican voters, he is the last untarnished hero of 9/11. Can they actually vote against him?

I am reminded of the politics of the post-bellum era - in which average-to-below-average Republicans in the North could be elected by "waving the bloody shirt," i.e. referencing their (seemingly) prominent roles in the Civil War to win the support of Northerners. In many respects, Giuliani's candidacy is similar (though I think there is a great difference in talent between Giuliani and the Gilded Age presidents). He is, in a certain sense, waving the bloody shirt of 9/11. Can the Republican Party refuse it?