Friday, November 21, 2008

The “What If” Fallacy

I belong to a union at my work place. Each month, my union local holds a meeting for officers, stewards, and any members who would like to attend. Normally, few people attend these meetings (I used to but they were so boring that I just wanted to pull all the hair out of my head). They want to encourage a large attendance, so as an incentive, they hold a drawing each meeting. Any attending member (there are 300+ members) stands an equal chance of winning the prize, which increases each month if not won. Currently, I believe the drawing prize stands at $250.

In order to further motivate members to attend meetings, my union decided to print out the name of the member that was drawn, whether or not they were present to win the prize, and display it on the bulletin board at work for everyone to see. The reasoning for this is obvious: if member “Sally G” had shown up, she would have won the prize, and how oh-so-foolish she was not to attend! So don’t look foolish like Sally G! Attend meetings!

But if member Sally G, who now feels thoroughly humiliated and angry that the union plastered her name on the bulletin board, had actually attended the meeting, would she have still won the drawing? Even if she hadn’t been an active participant and only said “hi” to a few people and sat down in the back, that would have been enough of a chain of events to completely alter the actions of those in the union hall. And by the time that the drawing was held, someone else’s name would doubtless have been picked. And Sally G also doubtless would have said to herself “These meetings are a waste of my time” and someone else would have been singled out for non-attendance.

Plus, who’s to say that someone may not have caused an accident with Sally G on the way to the meeting. There are also remote odds for that happening as well, but it is still almost like taking a drawing each time you go out on the open road. Plus, Sally’s presence at the meeting would have meant her absence in wherever she would have been, and that may have a probability of something bad happening as well.

But the main point is that you cannot surgically and retroactively insert yourself or another into a past situation and then ignore the effects that the new presence would cause on the chain of events. There was a very disturbing but profound Star Trek: The Next Generation episode titled Tapestry. In it Captain Picard, regretting the folly of his youth, wishes that he could go back to a specific point in his past and rectify a reckless decision he once made that got him into a fight and caused him to lose his heart (he “now” uses an artificial one). His “friend” Q pops in on the scene and shows him what would have happened had his wish been granted. It would have completely changed his life to something Picard abhorred. So he came to peace with his past decisions, even the "wrong" ones, and went on with his life (and his artificial heart).

There's nothing wrong with wanting to increase attendance. Just try to be a little more reasonable and respectful of those whose attendance you yearn for!

1 comment:

  1. Absolutely!

    Related misunderstandings:

    The bigger the "pot" gets in these sorts of drawings, the more people "play". Of course, the draw of a greater reward brings them in, but with more people there the chances of winning goes down (in the case where only the players can be drawn; it sounds like in your union meetings the odds of a particular person's name being drawn are constant).

    People don't understand the principle of "expected value". If you have a 1 in 100 chance of winning $100, the expected value is $1. If the pot goes up to $200 and that doubles the number of players, the expected value is still $1.

    At square dance clubs it's often customary to have a "50/50 drawing". When you come in, you pay a fee for the evening; let's say it's $8. They'll sell you a 50/50 ticket for the extra $2 (assuming that most people will pay with $10), and if you choose to do that, you're in the drawing. If your ticket is drawn, later in the evening, you get half the pot, and the club keeps the other half.

    A square dance club once wrote in a newsletter that they'd come up with a way to greatly increase their take on the 50/50: instead of selling one ticket for $2, they sold 5 tickets for $2. Lots more people bought them.

    The interesting thing, of course, is that selling everyone 5 tickets at a time doesn't change the odds at all compared with selling everyone 1 ticket at a time, if the same number of people buy tickets. And, of course, since more people are buying tickets, your chances of winning go down, even though you think you're getting a better deal. (The expected value, of course, is constant: no matter how many people buy tickets, the expected value is always $1.)

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