The US elections: the games politicians play

Game theory has interesting insights into perhaps the most bitter election campaign in living memory


The campaign has become a contest between Crooked Hillary (as coined by Donald Trump) and racist, misogynistTrump (as projected by Hillary Clinton). Photo: AP
The campaign has become a contest between Crooked Hillary (as coined by Donald Trump) and racist, misogynistTrump (as projected by Hillary Clinton). Photo: AP

Pundits say there has never been an election campaign quite like this US presidential election. The barbs have never been more vicious, the supporters of both sides have never been more certain, and, in the words of the poet W.B. Yeats: “The best lack all conviction, while the worst are full of passionate intensity.”

Game theory has analysed the process of voting and the strategies of political parties in some depth. One of the best-known results in this field is the median voter theorem which predicts that political parties tend to gravitate towards the ideology of the median voter. While this certainly does not seem to have happened in this election, a brief understanding of this result is useful.

Imagine voters distributed uniformly across the spectrum of ideology from ultra-left to ultra-right. Two political parties are searching for the right positioning, each knowing that voters will choose whichever party is closer to them. Without loss of generality, one can imagine one party starting from any position left of centre. In response, Party 2 would maximize its voter catchment by positioning itself slightly to the right of Party 1. Then, of course, Party 1 would sidle across to the right of Party 2, and this game of musical chairs would go on till both are situated right in the centre, where they split the votes. This position is called a Nash Equilibrium, a combination of strategies which constitute a mutual best reply, in the sense that neither player can do better by unilaterally deviating from its strategy given what the other player is doing.

In view of the tremendous ideological difference between Hillary Clinton and Donald Trump, this model is obviously inappropriate in the current context. An extension of the model works better. The interaction is sequential—first the two parties select their position in the ideological spectrum, then they decide how much to spend to attract voters after observing the other’s position.

In this model, a party can attract a voter despite his being situated further away from them than from the other party, provided that it spends a larger amount of money than the other party. At the Nash Equilibrium of this sequential game, the parties situate themselves at the opposite ends of the ideological spectrum in order to reduce the money they need to spend on attracting voters (if they are close together, then competition is high). In a paper published in Games And Economic Behaviour, political scientists Scott Ashworth and Ethan Bueno de Mesquita argued that the US presidential election, in which candidates are first selected from their parties based on their ideology, and then run costly campaigns against each other, has a structure that can justifiably be modelled by the extension of the median voter model.

However, while the two parties have very different ideologies in the present election, Clinton is situated more to the centre than Trump whose views on climate change, immigrants, trade and foreign policy place him at an extreme. Some would question whether he has an ideology at all given his inchoate and undeveloped ideas on most issues. In any case, the departure from the game theoretic prediction of maximal differentiation can be explained by a) the difference in the budgets of the two campaigns, b) the focus on personality rather than ideology, and c) the relation between the personal history of a candidate and the ideology they espouse.

Clinton’s war chest of over $1 billion is more than double that of Trump. Therefore, she can afford to position herself in the centre and increase competition. On the other hand, Trump with his limited resources needs to position himself at some distance from Clinton in order to get visibility. In other words, Clinton’s optimal strategy is to push out from the centre, while Trump’s is to pull in from the edges.

Second, the campaign has become a contest between Crooked Hillary (as coined by Trump) and racist, misogynistTrump (as projected by Clinton). In the process, ideologies and policy positions have become secondary. This has been most unfortunate as it has resulted in all the voters intensely disliking the personality (not the policies) of one candidate or the other. To the extent that this has blurred the focus on real issues and hurt Clinton more than Trump, her strategy of attacking Trump’s character appears to have backfired.

Usually in a US election, candidates espouse more extreme positions in the primaries, where they have to please the faithful in their own parties, than in the main election where they need broad-based support. Interestingly, Clinton has moved further to the left after the primary. For example, she espoused the minimum wage cause with greater conviction. This has largely been the influence of the popular campaign of Bernie Sanders, who fought the primaries from an ideological position left of Clinton. On the other hand, Trump has followed the rulebook and toned down his positions—for instance, on Muslims and Mexicans—after the primaries. Perhaps Clinton would have benefited from moving further to the left, picking up angry voters left out by economic growth—except that she would have found it hard to be credible given her stated positions over the course of a long career in public life.

It is unfortunate that a contest between two people who have such different views of what America should be degenerated into a slanging match. It reminds us that while big ideas are proven and discarded on the sweeping canvas of history, politics remains a clash of personalities.

Rohit Prasad is a professor at MDI, Gurgaon

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