Building A Glass House

© Copyright 2005, Paul Kislanko

One of the promises made in the latest round of knee-jerk "corrections" to the BCS selection process was increased transparency in the voting process. Most people took that to mean that the voters' ballots might be disclosed, and the only very minor step in that direction was the agreement that the final ballots would be public.

The debacle with the Associated Press poll in the final week of 2004, where AP voters who'd made their ballots public were pressured into "rigging the election" to the advantage (or detriment) of specific teams shows that that approach to "transparency" has its own problems.

Last year I suggested a better way to count poll votes that would provide transparency to the process and prevent any one particular voter from being able to affect the results. This approach (using a Bucklin vote-counting method instead of the Borda method) addresses the root cause of the problem that caused the Associated Press to pull out of the poll, even if all ballots were public.

But in the second week of the Harris Poll that replaced the AP, we learned that Harris Interactive has a ballot validation process that can change voters' ranks for a top 15 team, if the rank is too far from the mean rank. Last week I pointed out that the Bucklin approach would make this validation unnecessary.

But this week it occurred to me that even using the Borda method the process could be made transparent while preserving anonymous ballots in at least two ways. Even publishing the ballots wouldn't really help, since 114 voters times 25 ranks would pretty much be unintelligible to the typical fan.

The first approach to improving transparency would be to just publish the number of votes for a team at #2, #3, etc. the same way the number of first place votes is published today. The report would look something like this:

# Votes by Rank
14 Oct 2005 13:27:05 (US Central)

Note that we'd no longer have to guess if 51 points meant three voters got together and voted a team 111 voters thought didn't belong in the top 25 as their #9 choice or 51 voters thought the team was 25th. (This is the basic problem with Borda that causes it to not be used in any election that actually matters.)

This is still a lot more information than fans other than myself and Jerry Palm might want to have, but there's another way to accomplish the same objective.

If you must use Borda, Use it correctly!

The definition of Borda says "for each rank assign the value for a rank as the number of teams it is ranked higher than." In other words, with 119 teams, a vote for #1 should count 118, and a vote for 119th should count 0.

We can then represent the ballots shown above by just this table:

Ballot Analysis
14 Oct 2005 13:34:01 (US Central)

I've ordered the top 25 by Bucklin, and the "others receiving votes" by pure Borda. Notice that every team in the final top 25 is listed somewhere in a majority of voters' top 25. There may actually be fewer than 25 teams ranked on a majority of ballots, but no team that is ranked by a majority of voters in the top 25 can be left out because of a team that is ranked "too highly" by a minority of voters.

What contributes to the transparency without seeing the original ballots, or even the count of ballots is just using the 118, 117,... 94 assignment for #1, 2, ... 25. Since the fewest points than can come from any ballot for a team is 94, we know that any team with a score between 94 and 187 was listed on only one ballot and know exactly where on that ballot. A team with a score between 187 and 281 could not have been on more than two ballots, and so on.

The ballots used to demonstrate this example are actually 89 different computer rankings, as compiled by Kenneth Massey at College Football Ranking Comparisons. Since for the most part these do rank all 119 teams, the example was constructed by truncating each computer's "ballot" at 25.

The vote totals (and therefore pure Borda count) do not exactly balance, because some of the "voters' ballots" have ties, correctly expressed as consecutive ranks such as 3,3,3,6. My examples incorrectly calculate the Borda scores as 116,116,116,113, when in fact it should be 114,114,114,113, since the number of teams ranked below a given team should not include teams tied with it. I chose not to address that for the purposes of the demonstration.