Ice cream, apathy and the paradox of two party politics


Almost a century ago Harold Hotelling, the American economist, inaugurated the concept of “spatial competition”, recognising that businesses compete on position as well as price. Hotelling did not, though, actually use an anecdote often attributed to him of two boys arriving to sell ice cream on a long well-populated beach on a hot day. But posterity has agreed that the original article would have been much more vivid if he had.

The two boys would naturally gravitate together. If there were any distance between them, each would gain some of the other’s customers by moving closer. Yet each would find that their existing customers still reached them first. The result is inefficient — the average walk for an ice cream would be shorter if the carts were spaced further apart — but the result is inevitable.

We observe this clustering phenomenon in the similarity of product offerings from Hertz and Avis, or Unilever and Procter & Gamble. Australia’s “two airline policy”, now abandoned, led the two ostensibly competing companies to select almost identical schedules.

In his initial 1929 article, Hotelling noted that his analysis might be relevant to politics as well as economics, a thesis developed later by Anthony Downs, a political scientist. In a two-party system, policy positions would be close together, for the same reason as the ice cream sellers. From time to time, one party might move away from the middle ground but electoral arithmetic would drive it back to the centre.

Significantly, a three-party version of the game turns out to have no equilibrium. A stable outcome requires that one of the players is driven out. As the number of participants increases, however, the solution approaches one in which ice cream carts, or political parties, are evenly spaced along the beach. Where entry is cheap, as with proportional representation, voters have a wide variety of positions to choose. But where entry is costly, as in a first-past-the-post system, two parties with similar policies will be the norm.

The rise of democracy in the selection of party leaders has introduced a complication. The selection of US presidential candidates was once largely the prerogative of party bosses but is now the result of an exhaustive process of primaries. Leaders of the UK’s Conservative party were once chosen by men in smoke-filled rooms, while Labour left the decision to MPs; both now give the party at large the final say.

But politics is not quite the same as ice cream. You can only aspire to take charge of the political ice cream cart if you are the most popular candidate among your own customers. And the ill-served customers at the far ends of the beach are likely to be most voluble in expressing their views. Those nearer the middle, basking in the sun with an ice cream readily to hand, have little incentive to become involved.

The characteristics needed to win the leadership of your party are very different from those needed to win the leadership of your country. Extreme candidates are selected who lose races that mainstream candidates might have won. Parties revert, after years in opposition, to leaders such as the UK’s former Labour Prime Minister Tony Blair and Conservative Prime Minister David Cameron who are more popular with voters than with their parties.

Hotelling’s model illuminates the paradoxes of modern politics. The existence of two middle-of-the-road parties with immaterial differences is not a negation of democracy but an accurate expression of popular will. That outcome leads to complacency and apathy. But, given the prevalence of apathy, greater opportunity for engagement may lead to less democracy, not more, because those who do engage are necessarily unrepresentative. In politics as in economics, choice works best for you when you do not have to exercise it.


This article was first published in the Financial Times on April 8th, 2015.

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