Fishing for votes

As any statistician knows, Vice President Al Gore’s plan to recount votes in Democratic-majority counties has been intrinsically unfair.
During the last three weeks, Gore’s lawyers mounted a full-court press to force hand recounts in Broward, Miami-Dade and Palm Beach counties. Most recently, they sought a court order to hand count some 10,000 ballots in Miami-Dade County that did not register a vote for president when counted by machine.

In a televised speech, Gore contended that the hand counts were necessary to ensure fairness and accuracy. “That is all we have asked since Election Day: a complete count of all the votes cast in Florida,” Gore said. “Not recount after recount as some have charged, but a single, full and accurate count.”

If Gore got his way, however, the results would be anything but fair. Here’s an analogy that may help explain why.

Imagine you own 67 lakes, each populated with red and blue fish. Some lakes are bigger than others and have more fish. Some lakes have a greater proportion of red fish than blue fish and vice versa.

You are extremely wealthy and one fine afternoon, after a few too many beers, you bet an old fishing buddy a vast sum of money that there are more blue fish in your lakes than red ones.

To figure out who wins the bet, you must count the total number of blue and red fish in all the lakes. You decide to do this by draining each lake and putting the fish through a fish-counting machine. The machine counts live fish that are either red or blue. It rejects any fish that is over-colored (i.e. has red and blue stripes) under-colored (i.e. is neither red nor blue) or dead. Once the machine has counted the fish in a lake, the lake is refilled and the fish (dead or alive) are put back in. Regrettably, a few live fish die in the process of being counted.

After counting every fish in every lake you discover that there are about 6 million fish in all, and that the red fish outnumber the blue fish by a mere 1,700. Now sober, you blanch at the results. You call your buddy and tell him that the numbers are so close that you want to do a recount. Your friend thinks that’s reasonable and agrees. Once more, you count the fish.

Since the fish-counting machines aren’t perfect, the numbers come out a little different this time. Unfortunately, there are still about 900 more red fish than blue ones. You blanch again and wrack your brain for a way to win the bet.

Suddenly, you hit on a brilliant idea. Looking at the previous two counts, you notice that there are three huge lakes that are just swarming with fish, the vast majority of which are blue. What if you could drain just those lakes, pull out all the fish and hire teams of workers to count them by hand?

Furthermore, what if you allowed your workers to examine the fish that the machine rejected? After all, maybe some of the “dead” ones were really alive. Or perhaps some of the “uncolored” fish actually have a blue sheen when you hold them up to the light. Wouldn’t a more accurate count of those lakes be fair?

Not in this case. Since the number of blue fish greatly exceeds the number of red fish in those lakes, there are more opportunities for the machine to incorrectly reject blue fish than red ones. A more accurate hand count would thus add more blue fish to the tally than red ones. In lakes with mostly red fish, however, the situation would be reversed-with more opportunities for red fish to be rejected. There, a hand count would pick up more red ones.

As anyone can see–and as any statistician will tell you–selecting only lakes where blue fish are known to predominate is bound to yield biased results. Those results cannot legitimately be used to assess which color predominates in all the lakes.

The only way to get a fair and accurate tally is to count all the fish in all the lakes with uniform standards. But that has already been done and done again. And both times you lost. The only fair thing you can do is forget your scheme, pull out your checkbook and fork over the dough.

(William A. Dembski, a senior fellow with the Discovery Institute in Seattle, has a Ph.D. in probability theory from the University of Chicago. Mark Hartwig has a Ph.D. in educational psychology.)

Copyright 2000 Scripps Howard, Inc.