How much would you pay to change the stock market?

Through the first 623 days of their respective presidencies, the stock market has looked quite different for Donald Trump and Joe Biden. Under the Trump Administration, the S&P 500 (the most common index used when determining the market’s health) was up 28.18% on his 623rd day (which is better than the average 623 day period; the average 623 day period is about (about) 16%). Under the Biden Administration, the market was down, -0.21%. Factoring inflation, this real loss is much greater, but nominally, the difference between the two is 28.39%. Now, think about this in terms of how much you would be willing to pay to change the outcome of the Presidential election. Of course, who the president is doesn’t directly affect how the stock market goes up and down, but let’s assume you have a stock market obsession; you put $10,000 into the S&P 500 each year, track it constantly, and you think who the President is has a strong, strong correlation to how the indices perform. 

To determine how much an investor would be willing to pay, we have the equations MB > MC, MB = |V2 - V1|, B = MB, E(MB) = pB (E(MB) = Expected Marginal Benefit), and pB - C > 0. From ECON 2010, if MB > MC, the action should be done. So, the Marginal Benefit equals the amount you would pay for each candidate to win. For Trump to have won, the investor would pay $2,818, or the amount his portfolio would be greater (he believes) if Trump had won. For Biden to have lost, he would have paid $21, or the amount his portfolio is down. So, we plug these numbers in for V1 and V2, and get our MB. The MB is $2,839. We know from the reading that p’s value is 1 in 10,000,000; there is a 1 in ten million chance that your vote is the deciding vote. Therefore, pB = $2,839 * 1/10,000,00, or 0.0002839; less than 1 cent. The cost, C, we will assume is $17, or the median hourly wage in 2020. Plugging into our equation, we have $0.0002839 - $17 > 0, which is false. Therefore, voting is irrational even if you put $10,000 into the stock market in 2020. But, the paradox of voting states that there is a positive third variable, we’ll call it “u”, that stands for utility gained from voting, or civic duty. Plugging that in, the equation will look like pB - C + u > 0, meaning that u has to be at least $16.9997. This is important; the way I think about it is, would this investor be willing to pay $17 to put a Donald Trump sign in his front yard? If yes, then voting is rational for him. If not, then it isn’t and the voter is stuck with his portfolio’s losses.