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I'm on the Board of Directors of my Little League. We typically have about 35-40 players try-out for All-Stars. Managers, coaches and players (total of about 70) all vote for who they believe are the top 12 players. We total the votes and the top 10 vote-getters make the team. Is it statistically better to have voters only vote for 10 players vs. 12 players? It seems to me that statistically we are the most fair and get the truest result if we vote for the same number of players that are being awarded a spot on the team. By voting for 12, but only awarding 10 spots seems to cause some potential error. I want to make sure that the "extra" two votes isn't causing the system to be unfair or provide a result that is incorrect...especially when all 12 votes are counted the same, the votes are not "weighted". For example, if the voters all voted differently for their top 11 players but always voted the same player as their 12th and final vote, the 12th player would receive as many votes as the top player and make the team, whereas if each voter only voted for 10 players for the 10-man team, the 12th player would receive 0 votes and not even be in the running for a spot on the team.

Chad
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  • Welcome to our site! I think this would be a clearer question if you could explain what the "statistical error" might mean that you refer to at the end? – Silverfish Apr 02 '16 at 20:27
  • Not sure specifically what "error" I'm referring to...I guess that is what I'm asking, is there an "error" in our methods? – Chad Apr 02 '16 at 20:33
  • I have tried to make the title more specific - revert my change if you don't like my suggestion, or feel free to tweak my wording. As an aside, you definitely wouldn't want fewer votes per voter than spots on the team, in case there were a small number of outstanding candidates who got unanimous support from all voters with all votes, in which case your team wouldn't be filled! But what you are asking is subtler and more interesting. – Silverfish Apr 02 '16 at 20:34
  • Are you specifically concerned that people are being asked to vote people onto the team who, since they lie just outside the voter's top 10 but inside their top 12, the voter themself doesn't believe to be good enough to make the team? – Silverfish Apr 02 '16 at 20:36
  • Yes in a way you could say that...but, I'm more concerned about the fact that the 11th and 12th votes of a voter carry equal weight to the top 10 votes and that the last 1 or 2 spots on the team could be awarded differently if only 10 votes were cast per voter. Think of our Republican Primary Elections currently and how the results would be even more skewed if people could vote for 2 candidates instead of just 1 of the 17 candidates who began the process.... – Chad Apr 02 '16 at 20:39
  • It might be helpful to add some more contextual information - for instance do players have very defined roles in your sport? Are the all-stars meant to be the best "team" (in which case you might not pick some outstanding players if there are too many of them going for the same spot in the team) or is it purely the best players regardless of role? (In case I'm not clear: would an "all-star" soccer team with 6 goalkeepers make sense, if there just so happened to be an outstanding bunch of goalkeepers, even though you'd never play 6 goalkeepers in a real team selection?) – Silverfish Apr 02 '16 at 20:40
  • I understand your question and that is important for the team's success....but it is irrelevant to the question. Little League awards the 10 best players based upon majority vote and I want to make sure that by each voter casting 12 votes it isn't potentially skewing the results. – Chad Apr 02 '16 at 20:42
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    It is probably a good idea to edit some of those clarifications into the question, so that people preparing an answer don't have to read through the comments thread to find them. I've tried to ask what I thought the obvious follow-up questions might be, but wouldn't be surprised if other people have their own points they'd like clarified - please don't be dispirited if that happens. (If your Q doesn't get any attention for a few days, try editing it to bring the key points out. The site can get quiet on weekends/holiday periods.) – Silverfish Apr 02 '16 at 20:51
  • Your assertion there could be agreement on 12 but not 1 is silly. If two people don't agree on #1 it is likely the #1 will be on each other list. Now if you don't agree on #12 then a stronger chance it is not on each others list. If everyone chose the same top 12 then you would be in trouble. Just do 10. – paparazzo Jul 19 '16 at 11:18

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