Profit

I might be going too fast yesterday and the profitability of bribing an election may skip your eyes.

Let's suppose there are 6000 citizens in a country with a smooth distribution of age; voting for Party D would generate a total benefit of $600,000 to the society twenty years later. Equally shared by each and everyone, it means $100 per head. For simplicity, we assume the life expectancy is 80-year, and citizens could vote after the age of 20.

Now come the critical moment: A malicious Party C would try to take all the benefit for their own ($0.6M twenty years later, or around $128,700 immediately - assuming a discount rate of 8%). To bribe a sufficient number of vote, and suppose everyone could be reliably bribed, the cost would be:

• First, we need to get all 2000 votes from citizens over the age of 60. We can pay $1 for each, and the cost is $2000.
• The present value of $100 in 20 years is $21.5. Since we need another 1000 votes to win the election, the cost is $21500.
• Therefore, the total cost to win is $22500, and the net profit, if cashed immediately, is $106,200.
• (In fact, if we take it as a present investment of $22500 and a return of $600,000 twenty years later, the yearly return is 17.8% - as good as the performance of Warren Buffett.)

In reality, the cost would actually be lower, because the turn up rate of voting is never 100%. A detailed mathematical model predicts that the money Party C needs to bribe a sufficient number of voter actually falls rapidly if the turn up rate comes down to 50%. Readers with an obsessive personality disorder can try to work out the numeric details yourself.

Here, a determining factor of this profitable business may not be immediately obvious. Let me tell you tomorrow.