4 Why Should we Believe Politicians? Lupia and McCubbins – The Democratic Dilemma

GV917

Game Theory – the study of conflict and cooperation Game theory uses rational choice

assumptions in which each individual is trying to maximize their utilities subject to the behaviour of others

Lupia and McCubbins use game theory to develop a model of communications to address the basic problem:

When should individual’s trust the information they are receiving from others, particularly politicians who they do not know?

The Model

There are two players in the model - The speaker who is trying to persuade the principal to support an issue or to vote for a particular candidate

The speaker provides information about two alternative choices x and y (eg candidates or policies) and tries to persuade the principal to choose one of them

The key issue is when is such persuasion effective and when is it not effective?

Playing the Game The model involves three sequential moves – the order

of the moves is not relevant for the outcomes: (1) Determining if x is better or worse than y from the

point of view of the principal (2) Determining if the speaker has the knowledge to

accurately recommend x or y to the principal (he might not know what he is talking about)

(3) Determining if the speaker and the principal have common interests or antagonistic interests (if the speaker has antagonistic interests he might lie)

Given the three alternatives we can describe the whole choice situation in terms of a tree diagram, which sets out the alternatives

The Tree Diagram of the Persuasion Game

Branch (1) The First Dilemma – Does the Speaker know what he is talking about? The first dilemma for the principal is to

determine whether the speaker knows what he is talking about:

The probability that the speaker has the knowledge to give advice is k, and therefore the probability that he does not have the knowledge is (1-k)

Branch 2 The Second Dilemma – Do they have common interests? The second dilemma for the principal is to

determine if he and the speaker have common interests

The probability that they have common interests is c and therefore the probability that they do not have such common interests is (1-c)

Branch 3 The third dilemma – Is x better than y from the Principal’s point of view? The third dilemma is to determine if

alternative x is better than y, or if it is the other way round

The probability that x is better than y is b and therefore the probability that y is better than x is (1-b)

There are eight alternatives arising from this setup (k)(c)(b) (k)(c)(1-b) (k)(1-c)(b) (k)(1-c)(1-b) (1-k)(c)(b) (1-k)(c)(1-b) (1-k)(1-c)(b) (1-k(1-c)(1-b) For example, the first sequence is: speaker has the knowledge

(k), they both have common interests (c) and x is better than y for the principal (b). These alternatives are decided by ‘nature’ which is a way of saying that the players do not choose them

The Speaker makes his move

Both players now know the alternatives, so the speaker then makes his move:

For example he declares: ‘x is better than y’ or alternatively he says ‘x is worse than y’

Notice that he can choose one of these alternatives at each of the eight branches of the tree described previously – which gives 16 outcomes

The principal then has to decide whether to accept this message or reject it. Again he can choose either of these alternatives at each of the 16 branches, giving a total of 32 alternatives

How does the Principal decide what to do? He looks at the payoffs arising from each of the

thirty-two branches of the tree and determines which is the best one

For example, assume that we are moving down the branch in which

(1) The speaker knows what he is talking about (2) The principal and speaker have common

interests (3) x is better than y from the point of view of the

principal This branch has four outcomes:

Outcomes in the example

(k)(c)(b) B. X. – we are moving down branch (1) and the speaker says ‘x is better than y’ (B), and the principal believes him and chooses X. This produces a payoff of Z for the speaker and U for the principal {Z,U} – both gain.

(k)(c)(b) B. Y. – In this case the speaker recommends x but the principal does not believe him and chooses y. The payoffs are {0,0} for both the speaker and principal – neither gains because the correct advice has been rejected

(k)(c)(b) W. X. – speaker says ‘worse’ but the principal does not believe him and they end up with payoffs {Z,U}. These are positive because the principal is not fooled by the wrong message.

(k)(c)(b) W. Y. – speaker says ‘worse’ principal believes him with payoffs {0,0}. The principal loses from believing the lie.

What Should they do if they are on this branch? If they are on the (k)(c)(b) branch then it makes no sense for the

principal or speaker to choose alternatives which lead to zero payoffs for both of them, so this rules out (k)(c)(b) B. Y. and (k)(c)(b) W. Y.

From the principal and speakers points of view (k)(c)(b) B. X. and (k)(c)(b) W. X. deliver positive payoffs and so are preferred

But the speaker has no incentive to choose (k)(c)(b) W. X. – there is no payoff from lying – he might just as well tell the truth

So the equilibrium outcome on this particular branch is (k)(c)(b) B. X.

The principal believes the speaker because he thinks the speaker knows what he is talking about and they have common interests

What about another branch?

Suppose we change the assumptions and go down a different branch, so that assume

(1) The speaker knows what he is talking about(2) The principal and speaker do not have common interests(3) x is better than y from the point of view of the principalAgain this produces four branches, but this time the payoffs are different.

Outcomes on this other branch (k)(1-c)(b) B. X. produces {-Z,U}. That is the

speaker tells the truth (x is better than y) and the principal gains U because he believes it. However, the speaker now gets –Z, a negative payoff. This occurs because of the conflicting interests – he has in effect recommended something which is not in his interests. The speaker would have been better off lying to the principal

A better outcome for the speaker on this branch. (k)(1-c)(b) W. Y. produces {0,0}. In this case the

speaker lies by saying that x is worse than y and the principal believes him. They both end up with nothing because in reality x is better than y. Note that a zero payoff is better for the speaker than a negative payoff of –Z, so he prefers that outcome. This means that there is an equilibrium outcome on this branch because the speaker prefers it. He has an incentive to lie

Looking back through all the branches this means that if the principal thinks that he has a conflict of interest with the speaker he should assume that the speaker is going to lie.

The Equilibria of the Game

Backwards induction or working back through the tree diagram to evaluate all the possibilities produces two equilibria in this game – outcomes in which actors have no incentives to move away from.

(1) If the principal thinks that the speaker and he have common interests and also that he knows what he is talking about then the principal should believe him and be persuaded – they both end up with positive payoffs

(2) If the principal thinks that the speaker is not knowledgeable or that they have conflicting interests he should assume that the speaker will lie and not be persuaded – they both end up with zero payoffs

The Findings from the Model

Perceived common interests are a necessary condition for persuasion. This is not sufficient though.

Perceived speaker knowledge is a necessary condition for persuasion. This is not, however, sufficient.

Perceived common interests and speaker knowledge are necessary and sufficient conditions for persuasion

Some Experimental Evidence

Lupia and McCubbins tested these ideas in the laboratory. They had a speaker and a principal in the experimental setup, using undergraduate students at the University of California

The principal had to predict the outcome of coin toss (‘heads’ or ‘tails’) following persuasion by the speaker, who tried to favour one over the other

The principal received $1.0 for a correct prediction and in different setups the speaker received different amounts depending on his success in persuading the principal

Treatments - Interests

In one version of the experiment the principal knew that the speaker received a positive payoff if he predicted correctly (common interests).

In a second version the principal knew that the speaker received a positive payoff if he predicted wrongly (conflicting interests)

The experiments involved varying the speaker attributes to test the theory

Treatments – Speaker Attributes If the speaker saw the coin toss before saying anything

he was described as enlightened or knowledgeable and if he had common interests with the principal the expectation is that persuasion would be successful

If the speaker saw the coin toss but did not have common interests, the expectation would be that he would try to deceive the principal into believing they had common interests

If the speaker did not see the coin toss the expectation would be that he would not be persuasive, since he was not knowledgeable

The measure of persuasion is the number of times the principal’s prediction matched the speakers statement

Results

When the conditions for persuasion and enlightenment were satisfied persuasion occurred 89 per cent of the time (expectation 100 percent)

When the conditions for persuasion were not satisfied persuasion occurred 58 per cent of the time (expectation 50 per cent)

Conclusions

Game theory makes specific predictions about behaviour which can be empirically tested

There is considerable support for the Lupia and McCubbins argument

However, a laboratory experiment with undergraduates of the University of California has its limitations

There are systematic violations of rational choice which are observed in practice