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Monday, March 01, 2010

Canadian calculation

I watched the USA-Canada Olympic hockey final yesterday...it reminded me of the times we went to Hartford Whalers games in my youth. We were playing Boggle while watching, but it was a good enough game that we paused our own play a few times to watch theirs.

It was exciting when the team USA tied it up with moments to go, and I was a bit disappointed when Canada scored in sudden-death overtime to win the game. But only a little disappointed -- clearly, it matters way more to the Canadians than it does to us. I found myself simultaneously rooting for both teams to score. The question is, from a utilitarian perspective (i.e. the most good for the most people), was it really better to root for Canada?

I think we can hazard a scientific guess at this. Let's say that Canada's victory causes the average Canadian 10 units of joy. In relative terms, I estimate that a US win would have caused the average American 2 units of joy. (Much more for some, but I'm talking about the national average; there are plenty of people who don't care at all, while the vast majority of Canadians have at least some emotional involvement with their national team.) There are about 33 million Canadians and about 304 million Americans.

A simple calculation shows:

Canada wins
10 x 33,000,000 = 330 million units of joy

USA wins
2 x 304,000,000 = 608 million units of joy

So, you should still have been rooting for team USA. But note that if one were to assume that the average American experiences only one unit of hockey joy for every ten that Canadians experience -- a not-unreasonable assumption -- then you should have been rooting for Canada.

This calculation only takes into account the positive side of the ledger, however. Most Americans are well on their way to forgetting that USA even played Canada in the final; the Canadian psyche, on the other hand, would have been damaged for years. Let's assume that the disparity in defeat-induced sadness experienced by citizens is even greater than the joy disparity, -1 for Americans and -10 for Canadians:

Canada wins
[10 x 33,000,000 = 330 million units of Canadian joy] + [-1 x 304,000,000 = -304 million units of American joy] = 26 million net units of joy

USA wins
[2 x 304,000,000 = 608 million units of American joy] + [-10 x 33,000,000 = -330 million units of Canadian joy] = 278 million net units of joy.

That calculation still argues that a team USA win would have been the better outcome. Canadians might have a quibble with my numbers, though -- or possibly with my methodology.


Alex Starace said...

But I think you also have to grade happiness on a curve. I would say 10 units of happiness at once for one person is better that 5 instances of 2 units of happiness, either for the same person spread out over a couple of weeks, or for 5 people at the same time (though if the five people are in the same room, they can amplify each other's happiness, but let's assume they aren't).

I mean, I can bank 10 units of happiness for a whole week, but 2 units usually only lasts an afternoon or so. You know?

Teague said...

Okay, so units of happiness persist longer when they're clumped together, like the snow piled in the corner of the mall parking lot that sticks around until May. If we multiplied the units of joy by their duration at the sort of ratio you suggest, a Canadian win would take the net joy lead by a substantial margin.