Tuesday, September 16, 2008

Hall of Fame voters: too easily influenced by their colleagues?

Chris Jaffe takes a novel look at baseball Hall of Fame voting in a new Hardball Times article today.

He finds that the more votes a player gets one year, the more likely the writers who didn't vote for him will come around and vote for him next year. And the reverse: the fewer votes a player gets, the more likely the writers who voted for him will change their minds next year and drop him from the ballot.
Here's Chris's chart. The left column is the percentage of votes this year; the right column is the percentage are of dissenting voters who change their minds next year. (Actually, that's not quite true: the right column is the *net* percentage – even though the top group of candidates gained the equivalent of 31.9% of the previously-non-voting-for-them writers, that could be a combination of 45% gained and the equivalent of 13% lost, or some such.)

70%-75%: 31.9%
65%-70%: 21.0%
60%-65%: 17.7%
55%-60%: 11.3%
50%-55%: 12.4%
45%-50%: 3.8%
40%-45%: -2.0%
35%-40%: 4.6%
30%-35%: 0.03%
25%-30%: -2.8%
20%-25%: -2.8%
15%-20%: -6.0%
10%-15%: -7.7%
05%-10%: -7.3%

So it looks like voters are easily influenced by their colleagues.

What to make of this? One possibility is that the writers don't actually have strong opinions, and so they're easily swayed when their colleagues vote differently – that is, they're kind of reluctant to be dissenters. Another possibility, the one that Chris champions, is that the writers ARE fairly confident in their opinions, but that they are convinced and persuaded by the give and
take of the "grand national conversation" about who deserves to get in:

"Some would consider this a knock on the BBWAA and call it herd mentality. I beg to differ. It shows a willingness to listen to others, reexamine their position, and accept arguments others espouse. Simply put, it shows a willingness to listen, something I find commendable."

I don’t know much about psychology, so I'm not sure what's going on, but I suspect it's the same thing that drives changes in opinions on social issues. Thirty years ago, the idea that gays should have the right to get married was laughable ... but, over time, and very slowly, people started coming around to the idea, to the point where it's now mainstream (and legal, here in Ontario).

On gay marriage, I don't think people sat down and thought about it in any formal way ... it just kind of happened, as they slowly absorbed the chaging norms over time. Perhaps that's what's happening here.

Or perhaps not. Other suggestions are welcome.


UPDATE: here's another suggestion. Voters might think player X should be in the HOF, but, in a year with lots of candidates, they voluntarily limit the number of players they vote for. So 60% might vote for X now, and some of the other 40% join in next year, when there are fewer candidates and they have a vote to spare.

For instance, suppose every voter decides to choose only three candidates. But there are four worthies. The first year, B gets 90%, C gets 80%, D gets 70%, and E gets 60%. The next year, D and E are joined by A and F. Now A gets 90%, D gets 80%, E gets 70%, and F gets 60%.

So D and E have gained 10% each, just as observed. The 10% was the result of many writers wanting them in, but just not feeling they could spare a vote that year.

For this to work, I think you need the maximum number of votes per writer to exceed the (long-term average) number of worthy inductees.

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At Tuesday, September 16, 2008 10:06:00 AM, Blogger Ted said...

To this economist, HOF voting looks like rational information cascading.

Think of a model like this. Each candidate has some "true" worthiness w. Each writer gets some noisy signal of that worthiness. The signals are each of the same quality (variance) and independently determined -- basically, each writer's idiosyncratic take on things. If writers acknowledge that the signals others get about a candidate contain useful information -- which they should -- then when a writer finds out a candidate got a vote total higher than he would have expected given his original information, he should rationally revise his opinion favorably towards the candidate.


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