This paper is about introductory game theory. The upcoming election is the scenario, and the game is evaluated from the perspective of a student who needs to decide on the Presidential candidate that best serves his needs. There are different choices presented and evaluated pertaining to tuition cuts, taxes, and uncertain economic outcomes.
Game Theory
The scenario that I have chosen to write about is the upcoming election in the United States. The election essentially comprises a number of different ballots, including for President, for members of Congress and for Senate. There are sometimes other ballot initiatives as well, but for this discussion those will not be counted. The input of the election is the ballots that each voter casts. It will be assumed for simplicity's sake that every voter will cast a ballot for each category. The outcome will be the governance of the country at the federal level.
The structure of elections is such that there are a wide range of possible outcomes. We see polls in the newspaper about some of these potential outcomes -- who wins what states, etc. So there are a number of different ways to look at the election. For example, in the Presidential ballot, the electoral college system is used. For Congressmen and Senators, the ones with the most votes win. In the electoral college system, each state will have a set number of votes for President, and the candidate with the highest total of these votes will win the Presidency. It is worth noting that in this game, we can consider that there are four candidates including the Libertarian and Green Party candidates, but those latter two are highly unlikely to capture any votes in the electoral college.
One of the biggest decisions that a voter has is who to vote for. This is not always an easy choice as most voters have a number of different issues that are of concern to them. When the platforms of the political parties are evaluated objectively, it is highly unlikely that a voter will side strictly with a given party, so the voter can use to game theory to understand the best place to cast his or her ballot. To do this, the voter can evaluate payoffs.
Suppose Voter a is a college freshman. There are two issues that are important -- tuition funding and taxes. The student voter is only concerned about money, because he is economically rational. Tuition funding is an immediate priority, because Candidate a is promising additional funding for education that could see a net reduction in Voter a's debt load upon graduation. Candidate a is also promising no tax cuts, however, because his spending promises need to be paid for. Voter a figures there is a 75% chance that Candidate a's tuition reductions will be greater than the tax benefits that will be received, because new college graduates usually do not benefit from tax cuts that affect rich people. However, Voter a also knows that eventually he will make a lot of money and those tax breaks in the long run might help. There is a 25% chance that the tax cuts from Candidate B. will be bigger in the long run than the tuition reductions from Candidate a. As a rational person, the bigger the financial benefit will be a key deciding factor in the vote. Under this simple model, 75% is assumed to be the better place to put the vote.
Game theory can address far more complex scenarios, however. We all know politicians make promises on the campaign trail that they cannot keep. So consider the following:
Candidate a has a 20% chance of a $10,000 tuition reduction and a 10% chance of a $500 tax reduction. Candidate b has a 2% chance of a $10,000 tuition reduction and a 70% chance of a $500 tax reduction. The voter then must weigh these odds vs. The promised benefits. So for Candidate a: (.2)(10,000) + (.1)(500) =2000 + 50 = $2,050 benefit to the voter. For Candidate B: (.02)(10,000) +(.7)(500) = 200 + 350 = $550. The voter should vote for Candidate a because the expected payoff is much greater than for Candidate B.
Now in the real world this is likely to be a more complex scenario. Candidate a's platform might be expensive, and this could compromise the U.S. economy. Thus, the tuition credit might be great in the short-term, but taxes in the long run might increase and job prospects might be worse. However, the voter does not know if these things are going to happen. The same thing is true for Candidate B, because tax cuts are not free either. They also will exacerbate the deficit and could compromise the economy. There is disagreement over which policy prescription is going to be more likely to damage the economy. The health of the U.S. economy, however, is subject to a lot of variables, and one's own economic situation is only somewhat affected by the state of the U.S. economy. Still, the voter wants to vote in a way that increases the odds of a positive financial outcome.
There are a number of tools that can help to visualize the choice, but decision trees are not easy to draw in Word. Excel can be used to perform the same function. The voter can calculate that if the President spends too much money it will cost $40,000 in future tax increases and decreased job prospects.
Candidate a
Certainty
Value
Outcome
Certainty
Value
Total Odds
Total Value
Net
Tuition Cut
50%
$10,000
None
80%
$0
40.0%
$10,000
$4,000.0
Bad Economy
20%
-$40,000
10.0%
-$30,000
-$3,000.0
No Tuition Cut
50%
$0
None
90%
0
45.0%
$0
$0.0
Bad Economy
10%
-$40,000
5.00%
-$40,000
-$2,000.0
-$1,000.0
Candidate B
Tax Cut
80%
$500
None
50%
0
40.0%
$500
$200.0
Bad Economy
50%
-$40,000
40.00%
-$39,500
-$15,800.0
No Tax Cut
20%
$0
None
90%
0
18.0%
$0
$0.0
Bad Economy
10%
-$40,000
2.00%
-$40,000
-$800.0
-$16,400.0
The wild card is that the bad economy might happen no matter what the policies on taxes and tuition are, because there are other policies and other global factors that affect the economy. These other factors clearly affect the outcome, because if the economy is bad, neither candidate is going to have a positive outcome. Governmental giveaways will not help the voter if the economy is in the tank and earning power decreases. Candidate B's tax cut is especially useless. While the voter might be tempted to discount the bad economy from the decision, because it is not related to the decision, the odds of a bad economy do change with the decision and this is important. Tuition increases are less likely to affect American competitiveness because they are a small part of the budget; tax cuts are a much larger part of the budget and therefore if they are not matched by spending cuts are highly likely to have an impact on future American competitiveness. For those already in a good position, tax cuts look pretty good. For a student who is going to exit university with student loans and needs to be able to increase earning power rapidly, tax cuts are less important that economic competitiveness.
Thus, we can see how voting is a game. The voter first must make a decision about how important each factor is. The voter might decide that a non-financial factor is more important than money, and vote that way. But using monetary terms, the voter is asked to choose between a variety of financial policies. The outcomes of these policies are uncertain, so the voter must decide based on odds of the outcomes, and the size of the money at stake in the outcomes. A voter who is not a student and has no children who will go to college in the future would find Candidate B's tax cuts a better option. A voter who is a student or has children who will go to college would likely find Candidate a's policies more appealing, unless the size of the tax cut is much larger (so wealthy people might prefer B, while middle class and poor people would prefer a).
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