Waiter: Would you like something to drink with your meal?
Diner: What are my options?
Waiter: We have Pepsi and iced tea
Diner: That's it?
Waiter: Yes, I'm sorry, only those two choices
Diner: Ok, well I guess I will have the Pepsi then
Waiter: Oh wait, I just remembered, we have one more option -- in addition to Pepsi and iced tea, we also have Coke
Diner: Oh, well in that case.....I'll have an iced tea
Waiter: Ok, but if you don't mind my asking...if you are not interested in having Coke, why does offering Coke make you change your decision from Pepsi to iced tea?
Diner: It does seem a bit odd and illogical, doesn't it? I guess my brain must be wired a bit funny
As unlikely as this scenario sounds, it is played out every voting day in the American electoral system, which, it turns out, is also "wired a bit funny."
To see why, imagine that this time, the diner arrives with 6 friends, and they decide to save some money by ordering their beverage in a pitcher. Again, the waiter gives them a choice of Pepsi and iced tea. They hold a quick vote, and Pepsi wins 4 votes to 3. Once again, the waiter remembers that they also have Coke, so they vote again. This time iced tea wins with 3 votes, with 2 votes going to Coke and 2 votes going to Pepsi.
It should be easy to see why iced tea might win in such a scenario, even though it is exactly as "wrong" a choice as it was with the individual diner. The problem, of course, is vote splitting. Coke and Pepsi, being similar, split the "cola vote", resulting in an illogical choice.
This problem is identical to the one we saw at the Moose Lodge, and it is equally solvable. To solve the problem, the voters should -- instead of simply picking their first choice -- rank them in order first to last. For instance, imagine if the seven diners ranked them as follows:
You can now see that Coke is preferred to iced tea by a factor of 4 to 3 (4 people ranked Coke higher than iced tea, 3 ranked iced tea higher than Coke). 4 people picked Coke over Pepsi, versus 2 who preferred Pepsi to Coke. Since Coke beat each of the other candidates when compared "one on one", Coke is selected as the winner.
In the event that the waiter realizes that they are out of Coke, Pepsi would be the logical second choice, since 4 people selected Pepsi over iced tea, versus 2 people who preferred iced tea over Pepsi. Iced tea -- which was the winner when they held a "regular" vote" -- comes in dead last when using this improved system.