Who値l blink first? The mathematics of politics

Mathematics of politics  credit: Shutterstock
Mathematics of politics credit: Shutterstock

Prof. Rann Smorodinsky, Dean of the Faculty of Data and Decision Sciences at the Technion, applies game theory to Israel’s government and the protest movement.

The year is 1959. The US and the USSR both possess nuclear weapons, but each of them is deterred from using them, for fear that it will immediately lead to a nuclear counter-attack. If you’re s going to drop an atom bomb, it's best to be first, but it's also worth both sides knowing that that bomb will automatically trigger a response. The attacker knows there is no chance of coming out unscathed. If there is a chance of both sides avoiding dropping the bomb, so much the better for all concerned. This is a classic game theory scenario.

At that time, there was a debate in the US over whether to build shelters against nuclear attack. Would this be seen as an aggressive step that would encourage the Soviets to drop the bomb? Prof. Robert Aumann of the Hebrew University received a Nobel Prize in 2005, among other things for advising governments on such issues. In an interview with the scientific journal Macroeconomic Dynamics, he said, "If you build shelters, it's probably because you fear an attack. Why are you afraid of an attack? Maybe because you intend to attack, and therefore fear a counterattack. If you leave yourself exposed, it might mean that you don't think you'll be attacked in return, because you don't intend to attack. It's a reassuring message. And besides, if you build shelters, the price you pay for harm is lower, and then there is a greater chance that you will be willing to pay it, and that means the other side has more to fear."

This mathematical approach, devoid of moral judgment, characterizes the way in which game theory relates to political situations. In the 1960s and 1970s, Aumann was a consultant to RAND Corporation, a think-tank that advised the US government on managing its nuclear "game" with the USSR. In the end, both sides managed to do the right thing (hopefully all agree), and did not drop bombs on each other (but not before RAND Corporation was parodied in the movie Dr. Strangelove).

Can the political situation in Israel also be analyzed with the help of game theory? Absolutely, says Prof. Rann Smorodinsky, Dean of the Faculty of Data and Decision Sciences at the Technion-Israel Institute of Technology. Recently, he even created a YouTube video series about just that.

As with the game theory researchers of the 1950s, the "players" of today are still analyzed without judgment. "We treat even the act of lying in a neutral way; we call it 'strategic behavior,'" Smorodinsky tells "Globes". So what is the aim? To describe what’s happening, perhaps even make predictions.

Playing chicken, or which side can afford to lose?

What is the difference between a competition between a race between two cars hurtling towards a cliff, and IDF reservists threatening to stop volunteering, or doctors going on strike, should the judicial reform go through? In both cases the participants are playing chicken. Both cars zoom forward. The last to hit the brakes wins. But anyone who stops too late will tumble into the abyss. So, who will brake last?

According to game theory, the answer depends on the price of losing. Usually, the player who has a chance to win another time, or for whom the loss is not especially painful, will stop first. The one who is in no way willing to lose the game, for whom losing seems worse than or as bad as falling off a cliff, is the one who will stop last.

How does this analogy play out? Neither the government nor the reservists really want to harm the military's battle readiness. The doctors don't want to harm patients, and the government also doesn't want them harmed. But who sees the price of the alternative as higher? Are the reform legislators the ones who see themselves with a single opportunity they can’t afford to miss? Or are the reservists and doctors the ones who view the legislation as equivalent to falling off the cliff edge? Smorodinsky leaves it to us to draw our own conclusions.

The game of chicken is somewhat similar to the Judgement of Solomon, which has come up in recent political rhetoric. The "true mother" is the one willing to give up her child, provided that the child will not come to harm. The "false mother" is willing for the child to be harmed, provided he will not be with the other woman. That is how the real mother is revealed. So, who in our example is the person willing to destroy the country, provided that the other side does not get its way? Again, the interpretation is up to us. We hear the same rhetoric from both sides of the dispute.

But, says Smorodinsky, the basic assumptions of this analogy are not always valid. "If the real mother believes that the false mother will abuse the child, she will sometimes be willing to see him die as long as he is not with the other mother. We would say that, in this case, she has only one strategy: to demand custody of the child, even at the price of King Solomon cutting him in half. The false mother knows that the only strategy available to the true mother, and so she will withdraw her demand. In this case, King Solomon's decision is reversed. He must conclude that actually the mother who did not give up is the true mother."

Smorodinsky leaves it to us to make the basic assumptions according to our perception of reality, and reach a conclusion according to the theory he presents.

Strategic Polarization, or how attitudes become extreme

Israeli society has, in recent month, become more extreme. "Initially, most Israelis agreed that reforms of one kind or another were required in the system of government, and in the relationships between its three branches," says Smorodinsky. Then Minister of Justice Yariv Levin presented his proposal, which went further than much of the public intended. Since then, Israel has more or less split into two camps: those who don’t want any kind of change at present, and those who support the entire package that Levin proposed.

"Is this a change in values, or is something else going on here?" asks Smorodinsky. He suggests looking at these events using the Strategic Polarization model developed by American-Israeli professor Ehud Kalai and his son Adam Kalai. "Imagine two people with opinions on a certain continuum. For example, for the sake of simplicity, they have two adjacent plots that need to be watered, and ideally A would like to put the pipe a meter to the right of the middle, and B would want it a meter to the left of the middle. Now imagine that a mediator decides that the pipe should be exactly in the middle between the points that each of them wants.

In a case like this, if each person asks for their ideal point, the pipe will indeed be in the middle between the plots. But if A asks for the pipe to be 3 meters within his plot, and B asks for the one meter he really wants, then when they compromise on the 'middle', the compromise will fall exactly on the ideal point for A.

Suppose that B knows that A will propose the point three-meters inside his plot so that the settlement falls on the ideal point for him. Now B should demand that the pipe should be placed five meters into his plot, so that the midpoint is one meter into his plot, the ideal point for him. Thus, the parties keep demanding more and more extreme conditions.

Every time you hear that someone made an exaggerated claim in a set of negotiations just so that they could appear to be making a concession later on, they were actually thinking according to the Kalai model.

What happens if one side suddenly gives up? The side that seemingly gets everything it wanted will actually be very far from where it really wanted to be.

"It doesn't exist in the model, but I wouldn't be surprised if it sometimes happens. In reality, unlike in the game, people forget what their true ideal point is and get caught up in their own propaganda. The article is not about this situation, but you can imagine it. Sometimes politicians make extreme promises, and get stuck with them afterwards."

I know of another model, according to which two competing political parties should always compete over the center, because each sides more extreme supporters have no choice but to vote for the party closest to it, and so by appealing to the center, a party can win both the center and the extreme.

"It's called the hoteling model, and the example that illustrates it is two ice cream sellers on a beach. If every person on the beach buys ice cream from the seller closest to them, then it's worthwhile for the sellers to stay next to each other in the center. This is true during an election period, but the negotiations between the parties about the positions themselves take place after the elections. Someone who take an extreme position after an election may one day also be elected, and that might certainly moderate his extremism."

This is, of course, if he really believes that he is heading for another election.

The cake model, or who has more time?

One of the best known articles in game theory was written by Prof. Ariel Rubinstein of Tel Aviv University. He depicts two people who need to share a cake between them. Each side makes proposals to the other until one proposal is accepted and the cake is shared. But Rubinstein introduced another premise into the game: as time passes, in each round, the cake gets stale and less tasty. That is, the time element is also important.

Now the question is whether the two sides are the same. Is it important to one side to make a quick decision, while the other side has more patience? In such negotiations, the player who has time will win a bigger share of the pie.

So, who has more patience in the political game today? "There are those who say that Prime Minister Benjamin Netanyahu has less patience, because he would like to see a resolution in the political situation before he gets to his trial," says Smorodinsky. "In that case, it might be better for him to pass only part of the reform and shelve the rest, provided that this happens early. Others will say that actually it’s the protest movement that is in a hurry, because it is important to it to achieve something before the protesters get tired of protesting. It is possible to find other explanations for the levels of patience of the various players, and from this to derive the expected results".

Market forces, or do political parties do what's best for their voters?

The political system in Israel, which enables small parties to be elected and even tip the scales in the formation of a governing coalition, raises the question to what extent Israel's legislature actually represents the will of the people. Smorodinsky suggests considering a legislature consisting of 120 members and three parties. Two major parties have 55 seats each, while the third party has 10 seats. The largest proportion of the public would be represented if the two major parties allied, but, in practice, any combination of two parties would create a majority, so each party has exactly the same power in the parliament.

Quantitative analysis of political power was introduced by Nobel laureate Prof. Lloyd Shapley as early as the 1950s. "In professional parlance, we say that the 'Shapley value' of each party is one-third." We have seen this finding come to life in many of Israel's governments.

The situation gets a little complicated if we assume that some of the parties simply cannot join together, because the differences between their professed values are too great.

How does the electoral threshold affect this result?

"If we were to assume that we had two parties with 55 seats and then another 10 parties, each with a single seat, as opposed to one party with 10 seats, it would be difficult for any of the single-seat parties to tip the scales, and their power would diminish, while the power of the major parties would increase."

The assumption that parties will do what is best for the voters because otherwise they will not be reelected is an assumption based on market forces, but these basic assumptions can sometimes be challenged. In economics, says Smorodinsky, there are several known factors that prevent market forces from working. One is information asymmetry. If a seller, let's say of a used car, knows more about his product than the buyers, sometimes the buyer is unable to make the best decision for himself. Another factor is coordination. If several companies coordinate prices among themselves, buyers will not be able to obtain the best results, even if they have information and the right to choose.

In politics, there are cases of information asymmetry, especially when complex issues are being discussed. In this area, freedom of information, as well as independent media, help improve the symmetry between the citizen and the government. There are also cases where the parties have an interest in teaming up to achieve results not necessarily in the citizens' favor, instead of competing with one another for their attention and votes.

"Everyone recognizes the fact that public trust in the Knesset is low," says Smorodinsky, "and perhaps this is a sign that the public has identified a failure in this market."

Published by Globes, Israel business news - en.globes.co.il - on August 20, 2023.

© Copyright of Globes Publisher Itonut (1983) Ltd., 2023.

Mathematics of politics  credit: Shutterstock
Mathematics of politics credit: Shutterstock
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