Historically, there have been twenty-four GOP or Democratic conventions where the nomination contest went beyond the first ballot. This is a survey of these past conventions to see their overall tendencies, especially as they relate to a possible contested GOP convention this year.
Based upon past performance, if the Republican Convention has more than one ballot, the nominee will have a 42% chance of winning the general election. One could say that the electorate has a slight bias against voting for parties that are not united. However, this is not necessarily the case, as it could be fairly said that sometimes the party with the contested convention would have never had a chance of winning the general election to begin with (for example, the Democratic Party right after the Civil War). Nevertheless, many party leaders will be looking at past performance and will want to do everything possible to find a nominee on the first ballot, even if that nominee is not very plausible, on the theory that if the nomination fight goes into multiple ballots the winner will not have a chance at all in the general election (which, as we shall see, is not necessarily true).
There is also only a 42% chance that the leader on on the first ballot will be the nominee. Oddly, of the men who led on the first ballot and then went on to get the nomination, only 20% went on to win the presidency. That is, only two men went into a contested convention with the lead in the delegate count, and then won the general election: Grover Cleveland in 1884 and FDR in 1932. The bottom line is that most of these men were not very popular to begin with, and the nomination fight hurt them. Another way of looking at this is that only 8% of men who went into contested conventions with the lead in delegates actually became president. This does not bode well for the prospects of one Donald J. Trump. If he does not win on the first ballot, the odds are not good that he will be the nominee, and the odds are quite small that he will become president.
Oddly enough, the odds are higher in a contested convention that someone who is not leading in the delegate count will both win the nomination and become president. Fully 58% of the time, someone who was not the delegate leader won the nomination, and 57% of these men went on to win the general election. Or to out it another way, when it comes to contested conventions 33% of the time someone who was not the delegate leader at the beginning of the convention went on to get the nomination and then become president. These men were Lincoln, Hayes, Garfield, Harrison, Harding, Polk, Pierce, and Wilson. While 33% does not seem like good odds, they are much better than the odds of Trump becoming president if there is a contested convention.
One would think that the person who was second place in the delegate count going into the convention would naturally have a good chance of winning the nomination. And one would be wrong. Historically, only three men have placed second on the first ballot and then won the nomination. This is really bad news for Ted Cruz–essentially, he has only a 13% chance of winning the nomination, based upon historical norms. However, two of the three second place finishers went on to win the general election: Lincoln and Wilson. Based upon historical norms, then, it may be quite hard for Cruz to secure the nomination, but if he gets the nomination it is unlikely that a convention fight will hurt him in the general election.
What of those who were nominees coming into the convention, but who were not first or second in the delegate count on the first ballot? Eight of the final nominees (33%) fall into this category. However, only two of these men went on to win the general election: Rutherford Hayes and Benjamin Harrison. This means that at a contested convention, Marco Rubio or John Kasich (or even Jeb Bush, Rick Perry, or Scott Walker) have a better chance of getting the nomination than does Ted Cruz, but they will have no better chance in the general election than will Cruz, based upon historical norms.
Essentially, when it comes to contested conventions, the electorate gets a good look at all the people who were vying for election and generally decides it wants none of them. Of the candidates who had their hats in the ring at the beginning of a contested convention, only 25% went on to become president.
There is much better news for dark horses, however. A dark horse candidate is one who was not technically nominated for president at the beginning of the convention, yet was offered as a compromise candidate to break a convention deadlock. Of the fourteen men who went into a convention without a delegate count lead and then went on to win the nomination, six were dark horses. And of these six men, four actually went on to become president: Garfield, Harding, Polk, and Pierce.
Given historical norms, Trump and Cruz will do everything they can to lock up the nomination before they get to the convention, or to win on the second or third ballot. While the odds of Cruz achieving this are much smaller than those of Trump, there is every indication that this is in fact what he has in mind. There are ways to game the delegate selection process (a strategy Mitt Romney and Ron Paul were especially good at in 2012) to gain support, and already Ted Cruz has wound up with more delegates from Louisiana than Donald Trump, even though Trump won the Louisiana primary. A small but significant handful of delegates will also come into the convention completely unbound, and so Cruz will do everything he can to get their support. The more ballots there are at the convention, the less chance that either Trump or Cruz will become the nominee. Prospects are especially dim for Cruz in that respect.
John Kasich will want to employ a different strategy: He will want a deadlock. Then, he can offer himself up as either a compromise candidate or a kingmaker. However, based upon past norms there is absolutely no evidence that he will fare any better in the general election than will Trump or Cruz, so the only real rationale for supporting him is that he is not Trump or Cruz.
If the convention goes into multiple ballots, the best strategy for winning the general election would be to nominate a dark horse and then rally around that candidate. However, so many people have run for president this cycle that the GOP will be hard pressed to come up with someone completely new.