The paradox of the two frost It is an example, based on the economic model published by Harold Hotelling in 1929, which shows how in certain situations the search for Maximum individual profit may be in contrast with the interests of the community. Let’s see how two frosts that contend for customers on a beach will tend to occupy positions ever closer to each other, thus penalizing distant bathers. In political area This corresponds to two parties which, to conquer voters, end up settling on the same positions with consequent reduction from the freedom of choice by voters and possible increase in abstention. In both cases, the balance can be destabilized with the entry into the field of a new ice cream maker or a new party.
The paradox of the two frostai: what it is
The situation is this: let’s imagine being in August on one beach long one kilometer and crowded with swimmers scattered almost everywhere. Two ice creams, Who sell the same ice creams at the same prices, arrange on the beach with their kiosks in order to divide potential customers: the first is 250 meters from the beginning of the beach (left in the figure), the second 250 meters from the end of the beach (right).
Since theoffer of the two frosts is identical, And given that it is hot, the swimmers will choose to go to the nearest ice cream maker, along a maximum of 250 meters under the sun. In this initial situation, customers are equally divided, so if they use the distance as a criterion, assuming that the beach is populated evenly, half of the bathers will go to the left kiosk and half will go to the right kiosk.
At this point one of the two ice cream makers moves to the center so as to steal customers from the other ice cream maker. In this situation, to earn us is only the first kiosk, at the expense of both the second kiosk – which will have less customers – and at the expense of bathers because many of them, at this point, will have to travel more than 250 meters to obtain an ice cream.
To regain lost customers, also the second ice cream maker moves towards the center, Going to position yourself attached to the first ice cream maker. It seems counterintuitive, but in this way – attaching to the first ice cream maker – the second ice cream shop returns to have half of the beach as a customer! In fact, always using the criterion of customer-chis distance, finding both kiosks in the center, the right half of the beach will go to the nearest kiosk, that is, the one in the vehicle overlooking the right, while the left half of the beach will go to the kiosk overlooking the left.
What has changed from the point of view of bathers? What now they will have to travel more road! At the start Each batter could have bought ice cream along the maximum 250 meters, Everyone had an ice cream shop enough close to their umbrella. In the end one half of the bathers, if he wants ice cream, must travel under the sun More than 250 meters: some swimmers may even give up ice cream, which could bring, paradoxically, to one loss Of profit by the frosts with respect to the initial situation. The paradox consists precisely in the fact that there is no situation that is optimal at the same time for bathers and frosts.
What does the ice cream paradox have to do with politics
Let’s imagine now that i bathers represent the voters, then the community, of a country where there are alone Two parties whose political positions are represented by the position on the beach, from left to right. Voters will tend to choose The party closest to their positions, How swimmers will choose the nearest ice cream maker.
In the initial situation, each voter will be able to identify a party close enough to their positions. The voters of left they will vote the left party, those of right the right party. Subsequently the two parties will begin to move their positions to the center In order to acquire more safe voters and to reduce the range of voters between one party and another in the center. In the end, the offer of the two parties will be substantially the same therefore in reality the voters will only choose between two different ways of calling the same thing, their freedom of choice will therefore become fictitious!
In this situation It could also happen that many voters, considering themselves too far from the two parties renounce to vote, Just like the swimmers who find themselves at the left and right ends of the beach give up buying ice cream: here is the abstention party!
Can this paradoxical balance be broken?
The two frosts, once the center of the beach are reached, no longer move because, if they move, they would give in to the competition. For example, if the first ice cream maker moved a little to the left, he would immediately be followed by the second ice cream maker who would support him grabbing all those customers who came to visit between the two frosts. It is clear that at this point To the two frosts it is no longer convenient to move: We are in a stable balance position or that tends to remain such.
Let’s imagine now that in the central balance situation there is a Third ice cream which settles in the left side of the beach, these will cause big Damage to the first ice cream maker which will no longer have the exclusive on the bathers of the left end of the beach. A similar fate could happen to the second ice cream maker, the one on the right, if a fourth ice cream maker was placed even more on the right. We can imagine that, if they had the possibility, the first two frosts would oppose the arrival of the two new frosts.
Similarly in political areaany appearance of new parties It could break the balance and would be opposed by the two pre -existing parties. According to the paradox of the ice cream maker, therefore, we can expect that if in a electoral context There are only two parties – or coalitions – these besides flattening on very similar positions, they will oppose at the entrance to the game of other parties as they would risk breaking a convenient balance for them but not for the community of voters.
