This seems a perfect time to post this totally indefensible non-diary. I have a math problem that I need some help with and I know there are tons of highly analytical people on Kos, so I thought I would solicit your help. No, it is not for school or a test or anything like that. It is much more frivolous, but it's important to me.
I'm trying to come up with a formula to score a talent competition that gives the appropriate amount of weight to both the judges scores and the audience votes. I'm involved with a community theater group and we are running a talent competition as a fundraiser for the theater. We call it [Our town]'s Got Talent. It is somewhat like America's Got Talent, but the scoring is more like Dancing With The Stars. In other words, there are 3 judges that score the acts on a 1 to 10 scale (max score 30) and the audience also votes for their favorites. Everyone who buys a ticket to the performance gets one vote. The contestants therefore have an incentive to get all their friends and relatives to buy tickets and attend the performance in order to get themselves more votes.
Last year was our first year to do this and it was a great success. We sold out every night. This year we are holding the finals in a larger venue because we were so successful. But I was not happy with the formula we used to determine the winner. I'm hoping to improve it this year.
Our goal is to give the audience enough of an impact that they could theoretically determine the outcome. For example, on Dancing With the Stars, it is not uncommon that the person with the lowest judges' score is not the person voted off. In our case, we will not be voting people off one by one. We will have a finale with 10 contestants, with the top three winning cash prizes.
The formula that we used last year made it impossible for the audience to have a substantive impact. One of my associates came up with it. She said "let the audience be the 4th judge, with another 10 points to contribute to the total score." That sounded good to me, but the formula they used did not work that way at all.
What they did was give each contestant a percentage of the theoretical 10 points based on the percentage of the total vote they got. Because no contestant is likely to get an overwhelming percentage of the vote, the audience factor is actually quite negligible in that scenario.
We (the judges) realized that and agreed ahead of time to score generously, so that the audience would have the final say-so on the winner. We ended up giving 4 or 5 acts perfect 30 scores, and the one that had the most audience votes won.
I would like to have a formula that gives the audience vote more weight, so that someone who scored a 28 or 29 could possibly win over someone who scored a 30. It would make for better theater!
Here are the parameters--3 judges who can award up to 10 points each for each act. Ten acts. Audience of approximately 400 who can each cast one vote. How can the audience vote constitute between 25-33% of the total vote for each contestant?
Oh, and Happy Holidays! Eggnog for all who help!