Wisconsin’s Election Day went pretty much as expected, if you were following the prediction markets. On prediction markets around the world, people bought and sold contracts on any candidate winning any of the two elections; canonically, contracts are worth $1 if the candidate in the contract wins the election and $0 if the candidate loses the election. These contract prices are aggregated on my website, PredictWise.com, and turned into probabilities of any candidate winning any election. On April 4 those probabilities were 81 percent for Sen. Ted Cruz to win the most votes over Donald Trump and Gov. John Kasich in the Republican Wisconsin primary, and 88 percent for Sen. Bernie Sanders to win the most votes over Hillary Clinton in the Democratic Wisconsin primary. At the same time, Trump was 89 percent to win New York, the next primary on April 19, and 54 percent to win the Republican nomination. And, Clinton was 71 percent to win New York and 88 percent to win the Democratic nomination.
While the Cruz and Sanders wins were expected, their margins were slightly larger than expected. Going into Election Day, the markets also predicted margin of victory. On the Republican side the markets were about 50 percent that Cruz would win by 8 percentage points or more, and on the Democratic side it was about 60 percent that Sanders would win by 5 percentage points or more. Both candidates won by over 10 percentage points.
Cruz’s slightly stronger than expected victory affected Trump’s probability of winning the Republican nomination; he fell from 54 percent to 50 percent. If that number still seems high for someone who just lost Wisconsin in a landslide, post-Wisconsin Trump is still favored in New York at 89 percent and he is still the favorite in every primary the following week on April 26: Connecticut, Delaware, Maryland, Pennsylvania, and Rhode Island.
Probability of Republican Nomination
(Data: Betfair, Hypermind, PredictIt, and assorted Bookies; Figure: PredictWise)
Markets also help us dissect what winning could look like for Trump or any of the Republican field. The markets suggest Trump has an 18 percent chance to get 1,237 pledged delegates, enough to win the nomination automatically on the first ballot. And, he is currently give a 25 percent chance to win the nomination on the first ballot with a mixture of pledged and unbounded delegates. That means he is just 23 percent to win the nomination on the second ballot or more.
As no one other than Trump can win on the first ballot, another way to look at those numbers is that Cruz is 45 percent, Trump 30 percent, Kasich 13 percent, and Ryan 10 percent likely to win, conditional on a second ballot (which is 75 percent percent likely to happen). Of course, Kasich and Ryan are only eligible to win if the rules committee changes the rules to let in candidates that have not won the majority of delegates in eight or more contests; not surprisingly, Cruz is fighting really hard to keep that rule in place.
The Democratic nomination also moved a little, on the strength of Sanders’s stronger than expected showing. Clinton dropped from 88 percent to 87 percent to win the nomination. Like Trump, Clinton is expected to go on a tear following a rough patch of states. She is up to 76 percent to win New York on April 19, and expected to win in four of five April 26 elections (Rhode Island is leaning towards Sanders).
Probability of Democratic Nomination
(Data: Betfair, Hypermind, PredictIt, and assorted Bookies; Figure: PredictWise)
There is one more probability that matters, in many ways it is the only probability that matters: the likelihood of the eventual Democratic nominee beating the eventual Republican nominee in the general election. This number has held incredibly steady at 71-72 percent since March 16. This may seem surprising considering that Trump has fallen from 80 percent to 50 percent percent likely to be the nominee and Cruz has risen from just 11 percent to 31 percent. But, prior to his recent troubles, the market viewed Cruz as slightly less likely to win the general election, conditional on winning the Republican nomination; that is now equalized as Trump’s general election prospects would dampen if he limps into the nomination. Thus, the markets do not seem to think that swapping Cruz for Trump would improve the Republican Party’s chances of taking the White House in November.
Method Note: There is a three-step process for aggregating the prediction market data on PredictWise. Step 1: construct prices from the back/sell, lay/bid, and last transaction odd/price in the order book. I always take the average of the highest price traders are willing to buy a marginal share and the lowest price people are willing to sell a marginal share, unless the differential is too large or does not exist. Step 2: correct for historical bias and increased uncertainty in constructed prices near $0 or $1. I raise all of the constructed prices to a pre-set value depending on the domain. Step 3: I normalize the probabilities to equal 100 percent for any mutually exclusive set of outcomes.