Princeton Election Consortium

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Mitt Romney, game theory expert

March 19th, 2016, 7:34am by Sam Wang


John Kasich has a very narrow path to maximizing his chances for the Republican Presidential nomination (or a suitable consolation prize). However, it involves exercising self-restraint – and listening to the advice of that expert user of game theory, Mitt Romney.

Politicians can be excellent rational actors. This week, Mitt Romney urged Republican voters to support Ted Cruz. Previously, he suggested that Kasich and Rubio should only campaign in their home states, combining their support in each state. Do you suppose Romney really wants Cruz to be the nominee? Maybe…or maybe he just wants to prevent Donald Trump from getting a majority of delegates. Such an outcome helps Cruz, and it also helps Kasich…if Kasich does exactly the right thing.

In game theory, it is necessary to know what each player’s goals are, information and actions available to them at each decision point, and the payoffs for the various outcomes. In the case of the Republican nomination, we have the following information:

  1. Delegates are assigned to candidates according to state-by-state rules. They must vote for their assigned candidate on the first ballot, but after that they have the option to change their vote.
  2. A divided field lowers the threshold of voter support necessary to get a majority of delegates.
  3. If Donald Trump arrives at the convention with a majority of delegates, he will win on the first ballot.
  4. If Trump does not have a majority, his chances diminish considerably because of his outsider status.

What should the various players do? Based on recent calculations [Prospect] [PEC], I suggest the following.

Trump: It is in Trump’s interest for the field to remain divided. He may say that he wants a one-to-one showdown with Cruz. But in national surveys, GOP voters prefer Cruz over Trump by 15 percentage points. Broadly speaking, Trump can get 50% of delegates (or within a few dozen, which allows recruitment of uncommitted delegates) with as low as 35% popular support. So it is in his interest for Kasich to stay in the race in winner-take-all states. This was well worth the loss of Ohio’s 66 delegates. In fact, it was probably the cheapest way Trump could get that outcome.

Cruz: It is in Cruz’s interest for the field to narrow to a one-on-one race. For this reason, Cruz’s optimal actions last week were to campaign against Kasich in Ohio, and against Rubio in Florida. If Kasich drops out, Cruz could get 40% or more of total delegates. Therefore Cruz now wants Kasich to drop out – entirely.

Kasich: Kasich has no path to getting a majority of delegates. However, he does have a way to prevent Trump from getting a majority, which is different from what both Trump and Cruz want him to do.

First, Kasich should completely withdraw from winner-take-all states. Indeed, he should say so publicly, the way that Rubio pulled out of Ohio last week. In these states, he divides the “non-Trump” voter bloc, which polling suggests is about 55-60% of Republican voters. Therefore if Kasich does not drain support from Cruz, Cruz can take those states’ delegates away from Trump.

At the same time, Kasich should still campaign in the remaining proportional states, which are: Utah, the Northeast (New York, Connecticut, and Rhode Island), the Pacific Northwest (Oregon and Washington), and New Mexico.

Obviously, this path requires a lot of self-restraint. For one thing, Kasich doesn’t want Cruz to get the nomination. But I note that it is highly unlikely under any scenario for Cruz to get 50% of delegates.

Romney: Kasich’s strategy is exactly what Romney has recommended. Romney himself is carrying out the strategy – mostly. He advised Kasich and Rubio to pull out of one another’s home states. He campaigned for Kasich in Ohio. And now he is telling voters to rally around Cruz in Utah. This last step is not perfect – Romney could do even better by lying low in the proportional states.

In Romney’s case, we have the reverse problem. What is his eventual goal? It could simply be to stop Trump. But Romney may also be working in his own interest. An open convention also opens the possibility that Romney himself could emerge as the compromise candidate. After all, Romney does have a history of wanting to be President. The source of his credibility (former GOP nominee) is also grounds for suspecting his motives.

In graphical form, here is Kasich’s best strategy. The gray arrows indicate conventional political thinking.


Allowing a two-way race to unfold holds Trump to about 40% of delegates – and therefore an open convention. Cruz would also have approximately 40% of delegates, with Kasich and Rubio holding most of the remaining 20%. And the press gets the circus in Cleveland that it wants.

Tags: 2016 Election · President

41 Comments so far ↓

  • bks

    538 performs its own analysis and concludes that maybe Trump will get 1237 and maybe he won’t:
    http://fivethirtyeight.com/features/will-donald-trump-clinch-the-republican-nomination-before-the-convention/

  • jay sheckley

    Interesting.
    Perhaps it’s akin to what happened in Israel. 75% of voters voted against incumbent Bibi Netanyahu. But the popular vote –distributed among 4 opposition candidates– could not accrete to his ousting.
    So…what GOP outcome should Hillary want? Or Bernie?

    • Some Body

      No. Israel has a coalition parliamentary system. Parties are voted for, not individuals, and after all seats in parliament are allocated, a coalition is formed between parties to form the government. The largest party need not be the one that forms the government (thus, Netanyahu’s Likud was 2nd largest in 2009, with 3 fewer seats than this time around, but formed the govt. nevertheless), and smaller parties reliably belonging to one of the major blocks also reliably support the head of the block, not party, for PM (thus, a vote for N. Bennet’s ”Jewish Home” party, which is to the right of Likud implies support for Netanyahu as PM). As a matter of fact, Netanyahu’s continued Prime-Ministerhood was never in doubt in the 2015 campaign, and the only open question was about whether another party (Labour) will end up with a few more seats than Likud. It didn’t, but even if it had, Netanyahu would still be forming the coalition government. In short, you’re quite wrong about how elections in Israel work.

  • Peter T

    Kasich’s goals may not be so clear. He may hope for VP slot or something similar, but he probably has a range of secondary goals (most people do). Preserving his brand of Republicanism? Keeping Cruz out as well as Trump? Staying in with party elders or media barons in expectation of a retirement pay-off? His strategy has to include impacts on these, so concentrating on a single outcome with no regard for fall-backs is not sensible.

    • Some Body

      I read somewhere that he ruled out being Trump’s VP. How about positioning himself as ”next in line” for 2020?

    • Frank

      Really, I see Kasich not going further after his Ohio win. After Rubio suspended, Kasich became the next Great Hope for the GOP establishment. Polls just are not showing much movement toward him.

      Things look to be essentially a two-man race now, but Trump is the one who’s still ahead in most states, with Cruz taking a few others.

    • Matt McIrvin

      It looks to me as if, nationally, Kasich got a significant chunk of Rubio’s supporters. But so did Ted Cruz, and I don’t see Kasich really gaining on him.

  • Tom

    Excuse my ignorance…but Trump currently has 678 delegates…
    Shouldn’t the “New Delegates for Trump” red lines in the graph be 559 not 780?

    • Sam Wang

      Graph was pre-March 15. Post-March 15, it would look nearly the same except that the horizontal axis would have different numbers, since there are fewer new delegates to win.

      Probably in future versions I would make the horizontal axis “total final delegates.”

  • Warren D Smith

    The bigger issue which Wang here (and most media) leave unmentioned is, this all demonstrates the bad design of the VOTING SYSTEM.
    Trump (or perhaps Cruz) & Hillary are winning although polls show a majority of Americns disapprove each. Sanders & Kasich are losing even though they each are majority-approved.

    Also, relatedly, Sanders would do better vs Trump or Cruz, than Hillary would…

    So what we have, is the Repub & Dem parties, are intentionally using a voting system, which hurts their own chances of winning the presidency. Further, it is bad for the USA as a whole.

    If the GOP switched to IRV (instant runoff) that would not fix this problem in the sense that either Trump or Cruz would win the Repub nomination with IRV, so this “fix” still would be stupid for the GOP in the sense it still would intentionally nominate somebody with worse chances to win the presidency, i.e. the voting system intentionally chosen by the GOP would hurt the GOP, just like now. Ditto if the Dems switched to IRV; that also would not fix it.
    If however, we switched to approval (or presumably score) voting, which is simpler than IRV as well as more-wanted by people (say polls about what voting systems people like) that genuinely would have fixed the problem, at least in the present election.

    • Josh

      Without attempting to argue that the current system is perfect, it’s hard to remember sometimes that this isn’t the general election yet–it’s a series of quasi-local elections with many candidates, overseen by political parties. Your complaints about the current front-runners being disliked by many people are, to my mind, somewhat irrelevant at this point–the vast majority of Democrats who supported Hillary in 2008 still voted for Barack Obama in November.

      Furthermore, I’m not sure by what metric you can legitimately argue that BOTH parties are hurting their chances in the general by nominating their current front-runners. The GOP is a different story, but on the D side, Hillary has consistently led Bernie in national polling by close to double digits or more since the campaign began. She has won more votes than him and accumulated more pledged delegates than him, and all in a two-person race. It’s not like she’s winning a plurality of support–she’s clearly winning a majority of support. Is your argument that Sanders would be more likely to win independent and GOP votes in November than Hillary? I’m not sure how you could prove that…

    • Michael Hahn

      The US voting system IS broken, but I doubt that the political will exists to replace it with a better system. My own personal preference is for the German parliamentary system. In that system, half of the lower house is elected directly, based on districts and winner take-all modus, just like we do here; this is based on the FIRST ballot that voters cast. The other half of the seats in the lower house (Bundestag) are allocated based on the SECOND ballot that voters cast; this second ballot is cast for a party. The final makeup of the lower house is based on this second ballot; the seats are allocated such that the % of seats for a given party (directly elected and allocated) equals that parties % of the second ballots cast. A party must take at least 5% of the second ballots to have any seats, unless they gain seats by direct election in the districts (which seldom happens for smaller parties). The government is then formed by the party or parties that can command a majority of the seats in the lower house. What this accomplishes are several things: First, most political streams in society are represented in parliament, hence there is not as much drive to gerymander districts to maximize political power. Second, parties are forced to engage in compromise in order to participate in governance. A third benefit is that voters can split their votes, voting for a local representative that they like, and then cast their second ballot for the party that they feel best represents their overall political leanings. Fourth, everyone has a voice in parliament, and can exert political pressure on representatives through the threat to withhold second ballot support at the next election. Here, I am effectively disenfranchised, because I live in a gerrymandered district that will NEVER elect anyone of my political persuasion. And my representative in Congress can ignore me without fear of penalty, since his seat is secure regardless. It is the winner take all aspect of the US system that lies at the heart of the problems our system faces.

    • Just Dropping By

      Critiquing IRV based on the results it would produce if it was introduced partway through a series of elections where a different system was used in the earlier contests is rather ridiculous. Had IRV been used from the start I find it very unlikely that Cruz would still be in the race at this point, and only somewhat more likely that Trump would still be in the race.

    • Sam Wang

      We have some evidence of how an alternate-voting process would work. See my piece for The New Republic from July. Trump fares poorly as a second choice – that’s still true now, as I write in my American Prospect piece. So yes, a better approach might have been to start with such a process in the first place. As I wrote in July, such an approach might have yielded a more broadly acceptable outcome. The RNC might possibly consider a new approach in the future.

  • Amitabh Lath

    In order for this Kasich game theory to even have a chance, the delegates would have to vote to repeal the eight-state threshold (that only Trump has satisfied so far).

    Even if Trump does not have a majority of pledged delegates, there may be a majority that would not agree to rule changes.

  • Bert Katz

    Are there any winner-take-all GOP primaries remaining where Kasich is stronger than Cruz, so it would be better if Cruz dropped out in favor of Kasich?

    • Sam Wang

      Not at the moment. Kasich only leads Cruz in NY and RI. However, fresh polling data is lacking in the following winner-take-all states: WI, DE, IN, NE, MT, and SD.

    • Matt McIrvin

      Cruz will drop out in favor of Kasich shortly after I am elected queen of Romania.

  • Art Brown

    By my count, Trump (1) now has 55% of the delegates he needs, (2) had his best day since February (Nevada) last Tuesday, winning more than 60% of the delegates on offer, and (3) needs to maintain nearly that rate in the remaining races to get a majority.

  • Petey

    Also:

    “In the case of the Republican nomination, we have the following information … If Donald Trump arrives at the convention with a majority of delegates, he will win on the first ballot.”

    I think that would make his nomination much more likely, but I really don’t think we know that.

    We’re truly in uncharted post-’68 territory in Cleveland in terms of ‘bound delegates’ allegiance to their candidate on rules ‘test votes’.

  • Petey

    I concur with several of your commenters who make the point that while this game theory makes perfect sense on paper, it has serious problems in practice in accounting for voter motivation and Kasich momentum / press coverage.

    Also, one quibble I’m not 100% sure about:

    “First, Kasich should completely withdraw from winner-take-all states. … At the same time, Kasich should still campaign in the remaining proportional states, which are: Utah, the Northeast (New York, Connecticut, and Rhode Island), the Pacific Northwest (Oregon and Washington), and New Mexico.”

    Given that many of those “remaining proportional states” are still winner-take-most, isn’t Kasich competing in them doing work for Trump?

    (Personally, I think Kasich’s best strategy remains dropping out now, assuming that doesn’t result in lots of his delegates being re-allocated to Trump. He’d still be one of a small number of serious contenders in a multi-ballot convention.)

    • Joseph

      I agree that Mr. Kasich could well be thinking about the one big variable that’s still in play; momentum. After all, he’s still part of a three man race, and the race is a long way from over. And there are benefits to him that fall short of getting the nomination on the first ballot, especially if nobody does.
      All in all, I’d say Kasich supporters have to be somewhat upbeat at this point.
      Just to be clear, I’m not one of them.

  • Doctor Science

    Your analysis leaves out the key players: GOP voters.

    I think a majority of GOP primary voters (Trump/Cruz/other) share a burning hatred of the kind of rational calculation you’re suggesting is optimal for Kasich. Above all else, they want “authenticity”, the sense that the politician is driven by strong, sincere emotions.

    Objective facts may not matter to them, but emotional facts really do. I don’t think Kasich has the charisma (the performance ability) to perform the “Romney gambit” without coming across as insincere and calculating to GOP voters — and they will reject this in a firey rage.

    • Josh

      I see your point, but I have to ask: if Kasich is not on the ballot, voters can’t “reject” him by not voting for him because he’s…not on the ballot. So are you suggesting they would punish Kasich for his inauthenticity by voting for Donald Trump? That seems like a pretty difficult argument to substantiate.

    • Doctor Science

      punish Kasich for his inauthenticity by voting for Donald Trump?

      Essentially — I think would drive more voters to Trump as the Burn It All Down option, the one the GOP establishment is most opposed to.

  • Terje

    Re: Kasich’s options.

    Not all of the states described as proportional actually use proportionality.

    New York allocates 95 delegates. 14 of those are statewide distributed proportionally (with a 20% threshold).

    But the remaining 81 NY delegates are allocated 3 per congressional district. In the CDs, they are “winner take most” — 2 delegates in each district go to the district winner, 1 goes to the runner up (unless the winner gets 50% or no one else gets 20%).

    Rather than proportional, this gives a strong advantage to the candidate who runs 1st in the state.

    Washington state uses a system just like NY.

    CT is similar, with the winner in each CD getting 3 delegates, and the 13 statewide delegates allocated proportionally (among all candidates meeting the 20% threshold, unless someone wins 50%, in which case they get all delegates).

    (The other 3 described – RI, NM and OR) do award delegates based strictly on share of the popular vote.

    While it probably makes sense for Kasich to continue to campaign in those states (and potentially PA as well), I believe that it continues to make sense for Cruz to defer to Kasich (based on political strength on the ground and the way delegate rules work) in NY and CT (and potentially PA, MD, and NJ) if he hopes to deny Trump 1237.

  • Matt McIrvin

    I suspect that party opposition to Trump is softer that it appears, in the face of a situation where he has a strong plurality of pledged delegates. Even if he doesn’t have an outright majority, is the party really willing to risk alienating his large bloc of voters and sacrificing any possibility of a general-election win just to stop him? If the convention is actually contested, it’s more likely that they cut some kind of deal that nominates him on the second ballot in exchange for a more establishment-friendly VP pick and a mealy-mouthed promise to be less scary after the convention.

    • Matt McIrvin

      …Or, better yet, on the first ballot, if they can get some of the other candidates to release the delegates who are allowed to do so to vote for Trump.

    • Amitabh Lath

      Yes, I expect as Trump pivots to the general he will mitigate some of the harsh language, admonish the thuggish behavior, have some hard working legal immigrants up on stage, etc. The passive voice works well here “I’m sorry if anyone was offended…”

      I expect we will then see pundits who are writing “never ever” articles put out the “maybe we misjudged” and “things said in the heat of a pitched primary battle…” type columns.

    • Matt McIrvin

      There’s also the fact that the only alternative who actually has a lot of voter support, Ted Cruz, is even more disliked by some party-establishment Republicans, especially legislators.

    • Scott

      I believe the GOP has already accepted they will lose the White House this time and what this is all about (rumors of fielding a 3rd party candidate) is to give Senate and House candidates political cover in hopes of preserving seats. Where beneficial, some can back Trump, in other places they can back the 3rd party presidential candidate.

    • Ed Wittens Cat

      well…Trump isnt playing to the cheapseats– he is the cheapseats
      so GOP elite are terrified of alienating his base
      hes the “nostalgie” candidate
      Americans wont reject that– its really mostly like Weimar

    • Matt McIrvin

      I’m not sure they’ve accepted a presidential loss. The conservative political media seem still convinced that Clinton is about to be indicted over the email server issue. I think their chatter about it is actually increasing.

  • Terry Fitzgerald

    Sam,
    Has Smerconish been corrected on the pronunciation of your name i.e. WONG?

  • W. Mayes

    Is it not reasonable to believe that Kasich can also win these winner-take-all or winner-take-most states if the establishment rallied around him: Delaware, Pennsylvania, California, Maryland, Wisconsin, and Jersey? In fact, he could probably win many of them despite the establishment having already begun to rally around Cruz and having a three way race is necessary for Kasich to win at least Wisconsin.

    How many of the winner-take-all/most states is Cruz capable of winning? Given the political realities in these states and where Cruz has performed strongly so far, Pennsylvania, Wisconsin, South Dakota, Montana, Nebraska, and Arizona, are all good bets for Cruz. That’s… the same number as Kasich, but actually fewer delegates than Cruz. He has fewer delegates so far, yes, but Kasich could easily catch-up by competing in those winner-take-all/most states where he stands a reasonable chance in a three way race.

    And then moving to the proportional states that are left, it isn’t as if Cruz is going to do any better than Kasich in the sum of Utah, New York, Connecticut, Rhode Island, Oregon, Washington, and New Mexico.

    The last proportional state, West Virginia, on the other hand, is a battle between Trump and… how well Trump can beat his scores from adjacent Appalachian regions in the neighboring states.

    So why should Kasich be the one to drop out of the winner-take-all or winner-take-most states, given that he has just as many states as Cruz where he can theoretically win and when the balance of the remaining proportional states favors him, especially given that Kasich is actually the savior to the party in the general election, not Cruz (who the party elite mostly agree is worse, albeit in different ways, than Trump).

    Because Kasich needs a significant number of delegates to be the party nominee, which any analysis should assume to be his goal,* he needs to try to end the primary season with more delegates than Cruz. That’s only doable if you compete in the winner-take-all/most states where you are capable of winning. Thus, Kasich’s optimal strategy is to continue to campaign in any winner-take-all/most state that he stands a theoretically near equal (Pennsylvania, Wisconsin, California) or better chance of winning than Cruz (Delaware, Maryland, Jersey) while also competing strongly in the proportional states you’ve mentioned.

    *After all, as you’ve shown, a two-way race is likely to end up in a contested convention regardless, so unless he actually wants to be President, why would he continue to run?

  • Amitabh Lath

    This sounds good in theory but in practice how does a candidate drop out of only certain states? It has to affect his performance in neighboring states that share media markets.

    Trump seems to be turning to the general, challenging the WSJ about his turnout comparisons with Clinton, and ignoring primary debates with Kasich and Cruz.

    • Matt McIrvin

      One of Trump’s talking points is that he does well in head-to-head polls against Hillary Clinton. It’s not actually true, but he insists on it, usually cherry-picking some old outliers.

  • Eva999

    What you are suggesting requires a large degree of self-discipline, adherence to order, and a surrender of the nacissistic supply they have become accustomed to. I feel it likely the ringmaster has already lost control of the circus, he just hasn’t accepted it yet.

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