Proportional voting in the GOP primary won’t matter without proportional thinking

This year, in state Republican caucuses and primaries held prior to April 1, presidential candidates will earn delegates in proportion to the percentage of the vote they win in the state. So, for instance, if Mitt Romney wins the Iowa caucus January 3, which the prediction markets project with 34.9 percent likelihood, he won't take home all of Iowa's delegates--as has been the tradition in past primaries and caucuses. Likewise, the second place finisher in Iowa won't walk away empty handed--another departure from past form.

But what net effect will these changes create on the crucial early-primary race? According to the influential prediction market Intrade, the answer is likely to be "not all that much."

On Intrade, political horse traders buy and sell shares in primary outcomes--essentially wagering on the odds that Romney, Rick Perry, Herman Cain, Newt Gingrich, Ron Paul or someone else, will become the GOP presidential nominee. InTrade participants also weigh in on likely outcomes in key primary states such as Iowa, New Hampshire and South Carolina. So if, for example, we're consulting the market to break down just how decisive a Romney victory in Iowa would be, we can look at how closely the price of the Romney-wins-in-Iowa contract moves in conjunction with the Romney-wins-overall contract.

The correspondence is remarkably high. The likelihood of a Hawkeye State win for Romney rose and fell in the last fifty days in strong sync with his national likelihood: The correlation--a statistical measure expressing a relation that is not necessarily causal--between the two signals is 85 percent, with a 100 percent correlation meaning that the two signals moved in exact lock step.

The strong correlation also shows how much the two indices reinforce each other. The two Romney prices track so closely together in part because winning in Iowa will boost Romney's overall chances--but also because Romney's strength in Iowa increases in relation to his national popularity.

Perry, Gingrich, Cain, and Paul all have high correlations between their Iowa and national prospects: 93, 97, 57, and 42 percent, respectively. (In statistical terms, even Paul's comparatively weak 42-percent alignment represents a significant correlation.)

We can go one step further to make an educated guess of what would happen if Romney wins in Iowa.This comes about via a technical analysis known as a logistic regression. Under this approach, variant points in the national-Iowa outcomes for Romney will project forward to reflect a 100 percent likelihood of the former Massachusetts governor winning the Jan. 3 caucus vote.

One thing is clear in this model: What happens in Iowa certainly won't stay in Iowa. If Romney manages to prevail there, the model projects he would have as high as a 90 percent chance to win the national contest. If, on the other hand, he finishes second or worse, Romney would enter New Hampshire with only a 40 percent chance to earn the GOP nomination.

If Perry wins the first-in-the-nation caucus instead, he'd have an 80 percent chance of eventually becoming the Republican nominee; if he fails in Iowa, his chances nationally fall to 5 percent. If Cain, Gingrich or Paul don't win in Iowa, their campaigns would plunge into something approaching code-red status, according to this model. Their odds of coming back to win the nomination fall beneath 5 percent in the absence of an Iowa victory.

Keep in mind that the regression model doesn't work the way that the campaign or the news cycle does in real time. That is to say, the math involved here makes no qualitative distinctions between the way that Iowa stands to affect the national race, or how the national scene reciprocally shapes the Iowa field. That being the case, the regression almost certainly exaggerates the overall impact of an Iowa win.

There are two other important notes of caution. First, extrapolating a trend based on data is not an exact science. Rather, take it clearly for what it is: an estimate or educated guess, nothing more. Second, in constructing this model, I collected the data over the last 50 days. Over that time, all sorts of factors in the race have changed dramatically--yet the logistic regression machinery assumes all data points reflect current knowledge. These cautionary notes translate into a simple watchword: Don't take the precise numbers too seriously, but do heed the overall message--early states will still have tremendous influence, despite the new proportionality rules.

We could get a better indicator of Iowa's impact if a prediction market were to directly assess the chance that Romney will win in both Iowa and the nomination--but, alas, that market doesn't exist. When we launch our prediction games on The Signal, we plan to feature many such combined A-and-B predictions and more: Stay tuned.

The Republican National Committee hoped proportional assignment would extend the race beyond the first few states, allowing broader participation from voters and greater media exposure for GOP candidates. As Stephen Ohlemacher wrote in the Huffington Post, "don't look for a quick winner in the race for the Republican presidential nomination." Ohlemacher quoted one RNC member, Bob Bennett of Ohio, saying that "I could see [the primary] going deep into April with a two-man contest." In 2008, a similar proportional-voting setup in the Democratic primaries did seem to draw out the two-person race between Hillary Clinton and Barack Obama.

On the other hand, voters and the media tend to think in all-or-nothing, not proportional, terms. Even Clinton's chief strategist and pollster in 2008 reportedly forgot that the Democratic primary was proportional. The notion that "winning is everything" is deeply ingrained in sports and politics alike. Fans of the World Series champion St. Louis Cardinals consider being one strike away from losing--twice--a mark of strength rather than good fortune. And George W. Bush's chief strategist Karl Rove's reputation as a genius was certainly bolstered by his narrowest-of-narrow victory in the 2000 presidential election.

So, in short, if on January 4, headlines shout "Romney wins Iowa" and voters start to think of the former Massachusetts governor as the presumptive nominee, whichever candidate ends up claiming second place will have a handful of delegates--and not all that much momentum going forward.

David Pennock has a Ph.D. in computer science from the University of Michigan and currently heads the algorithmic economics group at Yahoo! Research. Follow him on twitter @pennockd.

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