April 26, 2016

Chopping the Primaries

As another set of presidential primary results come in tonight, it is interesting to note how the different delegate selection systems used by the Democrats and Republicans have had significantly different effects on how each party's eventual candidate will be selected. Let's look at these effects by using poker tournaments as an analogy.

Each state is essentially a separate poker tournament, offering a prize pool of delegates. The size of the prize pool (number of total delegates available) will vary based on the nature of the tournament. For example, some tournaments have smaller buy-ins or fewer participants, and have a smaller prize pool, while other tournaments have larger buy-ins or more participants, and have a larger prize pool. Under this analogy, California is the Main Event of the presidential primary season. You have to win a lot of smaller tournaments (or a lot of Nebraskas and Delawares) to net as many delegates as a win in the Main Event.

Even more important than the prize pool, however, is the payout structure. On the Democratic side, all states award delegates on a proportional basis—win 55% of the vote, get roughly 55% of the delegates (in states with small numbers of delegates, the delegate counts may deviate slightly due to rounding, such that a 52%-48% "win" results in an equal split of delegates). On the Republican side, however, early primaries were proportional (with a qualifying threshold), while most later-stage primaries are winner-take-all or winner-take-most affairs. In those states, a simple plurality of the vote—maybe as little as 40%—can win 90-100% of the delegates.

Viewed as poker tournaments, the Democratic primaries essentially are structured such that the candidates are required to "chop" every primary. As my poker-savvy readers know, chopping is an agreement to split the prize pool rather than playing out the tournament to its end. Chopping is common in poker tournaments, and is a method for reducing variance (being the chip leader is great until a couple of short stacks get lucky and knock you out with a small payout). Chopping is usually tied to chip stack size, recognizing that players with more chips have a better chance of winning. One basic method of chopping is a "chip-chop" where every player is paid last place money, and the remaining prize pool is divided proportionally to chip stack size. So, players with larger chip stacks get larger percentages of the prize pool, but everyone gets more money than last place money.

The Republican primaries—at least those remaining—are more akin to poker tournaments with top-heavy payout structures. Poker tournaments with guaranteed payouts (such as the WSOP "Millionaire Maker") often feature large payouts to the winner or top few players, with little or no prize money for lower finishers.

These structural differences are critical to the underdogs in both races. On the Democratic side, the primary was essentially decided by Super Tuesday, when Hillary Clinton opened up a sizable pledged delegate lead. Although Bernie Sanders has won numerous primaries and caucuses since then, most of those were in smaller states with fewer delegates. Even worse for Sanders, the proportional award of delegates made it difficult for Sanders to make an appreciable dent into Clinton's delegate lead because Clinton will pick up sizable numbers of delegates even in states she loses. Effectively, Sanders can never come close to sweeping a state's delegates. Based on projections by FiveThirtyEight.com, Sanders will likely need to win 65% of the delegates in the late-stage Democratic primaries, which translates into this essentially impossible scenario:
"Based on these estimates, Sanders would need to beat Clinton by 26 percentage points in California, 28 points in Indiana and 16 points in New Jersey, all states where he trails Clinton in polling averages. He’d also need to win Western states like Oregon and Montana by 50 or more percentage points."

~ FiveThirtyEight.com
By contrast, the top-heavy structure of the late Republican primaries offers Ted Cruz an opportunity to quickly close the delegate gap on Donald Trump if he is able to score even narrow wins in most of the larger remaining Republican primaries. Even though that scenario is unlikely to lead Cruz to a majority of delegates, Cruz still has a decent shot of winning enough delegates to deny Trump a majority of delegates, enabling Cruz to make it past a first ballot and into a scenario where delegates would no longer be pledged to Trump and could throw their support to Cruz (or John Kasich or Marco Rubio).

In short, Sanders could close out the remaining primaries on a string of 60%-40% victories and handily lose the Democratic nomination, while Cruz could close out the remaining primaries on a string of 40%-35%-25% victories and win the Republican nomination. Of course, the most likely scenarios are for Clinton and Trump to score solid victories in most of the remaining primaries (starting tonight) and wrap up majorities of pledged delegates prior to the party conventions. But the difference in delegate selection structure means Clinton is essentially on cruise-control while Trump will be in a dogfight to control Cruz.


  1. Nice analogy, Grange. I guess if you try hard enough, you could relate anything to poker.

    For example, you could say that Cruz went "all-in" picking Fiorina as his VP now, even though it may have been smarter to wait and possible make a deal with either Kasich or Rubio to trade the VP slot for their delegates and put him over the top.

    And if Trump gets really, really close to getting the nomination but is denied, can we say he was sucked out on?

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