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By Jay Cost

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On McCain's Voting Coalition

An argument being proffered by Romney supporters is that McCain's victories in the early states have been due to the conservative vote being split among many candidates. By this thinking, McCain would have lost South Carolina and maybe Florida if conservatives had coalesced around a single anti-McCain candidate. Michael Medved commented on this theory yesterday. I would like to toss in my two cents, as this sort of matter is up my alley.

At first blush, this theory might seem compelling. However, if we take a closer look at the exit polls in New Hampshire, South Carolina, and Florida, we can see that this is actually a problematic assertion.

First of all, we have to clear away some of the theoretical underbrush. What we are talking about here is the idea that the electoral results to date display social irrationality. Is this possible? Absolutely.

Suppose that you prefer ice cream over pizza, and pizza over hamburgers. If you were given a choice among all three, you would choose ice cream. If you were given a choice among just ice cream and hamburgers (with pizza excluded), what would you choose? Again, it would be ice cream. The choice between ice cream and hamburgers is independent from your feelings about pizza, which are irrelevant. So, your choice is independent from irrelevant alternatives.

This is a characteristic of individual rationality. Can we expect society as a whole to act rationally in this way? If we all take a vote on ice cream, pizza, and hamburgers - would we prefer ice cream to hamburgers regardless of whether or not pizza was an option? If pizza does change the preference between ice cream and hamburgers, can we say that society has chosen rationally?

These questions are part of a general subject known as "social choice." It has been of interest to smarty pants for centuries, especially French smarty pants. In the 18th century the Marquis de Condorcet and Jean-Charles de Borda argued over how to design voting systems that avoided irrational outcomes like the one highlighted here. Of course, leave it to an American to prove that the French were wasting their time! This is exactly what Kenneth Arrow did in 1951 with his impossibility theorem (a.k.a. Arrow's Theorem). Arrow later won a Nobel Prize in Economics for his achievement.

What Professor Arrow did was devastatingly simple. He identified a handful of basic criteria that we would expect any rational voting system to meet - and proved that no system could meet every criterion every time. We just finished talking about one such criterion - independence from irrelevant alternatives does not always hold when we move from individual choice to collective choice. Depending on how we conduct the vote, society could change its preference from ice cream to hamburgers because pizza was included or excluded as an option.

Romney supporters are using this concept to argue for their candidate. The final result in Florida was McCain > Romney > Giuliani > Huckabee. According to their argument, if Giuliani and Huckabee were not on the ballot, the collective choice between McCain and Romney would have been reversed. Irrelevant alternatives were not independent - as this argument goes. Take the other conservatives off the ballot, and Romney would have defeated McCain.

Let's dig into the exit polls from New Hampshire, South Carolina, and Florida to see exactly whether this claim bears out.

As I argued last week, feelings about the Bush administration have been influential in determining primary vote choices to date. We should note two distinct features about the vote distribution of Bush/anti-Bush voters. First, McCain consistently wins those with negative feelings toward Bush, and consistently loses those with positive feelings toward Bush. Second, most Republican primary voters have positive feelings toward the Bush administration.

So, for instance, in Florida:

- 68% of Republican voters claimed support for the Bush administration; 32% did not.

- McCain won 31% of Bush supporters, 45% of Bush opponents.

- Romney won 35% of Bush supporters, 23% of Bush opponents.

- Giuliani won 16% of Bush supporters, 12% of Bush opponents.

- Huckabee won 15% of Bush supporters, 10% of Bush opponents.

This seems to bode well for the anti-McCain argument. If you fold up the pro-Bush vote into a single candidates in Florida, the pro-Bush candidate might well have beaten McCain. Perhaps McCain has been winning only because the pro-Bush vote has been split among multiple candidate. This would violate the independence from irrelevant alternatives criterion. Taking all but one of the conservatives off the ballot, by this logic, would flip the results in Florida.

This conclusion is hasty. Romney surely won more pro-Bush voters than McCain, but he did not win that many more. McCain, for his part, won many more anti-Bush voters than Romney did. This could make a big difference.

Let's drill this down with some mathematical analysis:

(1) Suppose a two-way Florida race between Romney and McCain in which (following the exit poll) 68% of voters are pro-Bush and 32% are anti-Bush. Also, suppose that the key variable in determining where the voters of the now excluded candidates go is their feeling about Bush.

(2) In the actual race, McCain beat Romney among anti-Bush voters in a multi-candidate field, 45% to 23%. In a hypothetical two-way race, the proportional result would be 66% to 34%, McCain.

(3) In the actual race, Romney beat McCain among pro-Bush voters in a multi-candidate field, 35% to 31%. In a hypothetical two-way hypothetical race, the proportional result would be 53% to 47%, Romney.

(4) In a hypothetical two-way race with proportional distribution of pro/anti-Bush voters, McCain's vote share would be calculated as: 66% X 32% + 47% X 68% = 53%; Romney's vote share would be 100% - 53% = 47%. Thus, McCain would win a hypothetical two-way race determined under these conditions.

The same goes for South Carolina and New Hampshire. I'll spare you the mathematics and just conclude that if you turn those races into two-man contests following the same rules I used with Florida, McCain would still win both states against his strongest opponents.

Perhaps using feelings about Bush is not the best way to re-allocate votes in a two-man race. Perhaps the best way is via ideology. Accordingly, I re-ran these calculations dividing the electorate into four ideological groups: liberal, moderate, somewhat conservative, very conservative. Once again, I folded the actual race into a hypothetical two-way match up, allocating voters by ideology proportional to how they supported McCain and Romney (or, in South Carolina, Huckabee). Once again, I found that McCain wins all three states.

I would also note that if you wanted to reallocate the vote based upon professed second choices - you would find the same result in Florida. Most Huckabee voters there claimed McCain as their second choice. Romney and McCain were essentially tied among Giuliani voters. Unfortunately, the same question was not asked in New Hampshire or South Carolina.

As I hinted above, this does not necessarily mean that the anti-McCain theory is wrong. Take a look at the Florida example. Among pro-Bush Florida voters who actually supported McCain or Romney, 53% went to McCain and 47% went to Romney. So, that was how all pro-Bush voters were split in the hypothetical two-way match up. However, maybe pro-Bush voters would have broken more heavily to Romney. That could alter the results, depending on how they go. If they go by at least 58/42 - Romney would defeat McCain.

While this is possible, it is hard to argue that it is likely. If anything, voters might break more heavily to McCain than my baseline model implies. According to the latest Pew poll, Huckabee voters have a +36% favorable rating of McCain, but a -4% rating of Romney. It is hard to argue that Romney would take more Huckabee voters than McCain, which is actually what the baseline predicts. The same goes for the Giuliani voters - who in the January Pew poll were more favorable to McCain than to Romney. So, if we alter this assumption to reflect the Pew results - we might see McCain's lead grow.

And so, I do not think one can argue that McCain's wins have been dependent on a divided field. Independents, moderates, and Bush disapprovers have certainly formed the core of McCain's voting coalition. However, McCain has done what most winning candidates do: win his base by large margins while stealing plenty of voters from the other guy's base. McCain does not win conservatives or Bush supporters outright - but he has done well enough with them that he could probably win New Hampshire, South Carolina, or Florida in a head-to-head match up.

I think the Romney supporters are on better empirical ground to argue that their candidate's problem has been that Bush supporters and strong conservatives simply have not made up a sufficiently large share of the vote - and that "true" Republicans need to "wake up." Accordingly, their goal should be to turn out more of their voters. Maybe they will be able to do this in California today.

Relatedly, this highlights McCain's potential weakness. While it is difficult argue that a narrower field would turn any of McCain's wins into losses, the fact remains that each race would probably have been tight. Under my assumptions, McCain never would have won more than 54% of the vote - and his victory in South Carolina over Huckabee could have shrunk to a little less than one-half of one percent. So, McCain has been building a voting coalition that can trump the coalitions of other candidates - but not by much. If the anti-McCain forces could have turned out more of their voters in the other states, they might have won.

-Jay Cost