Why Single Voting is Unfair

While this idea first popped into my head many years ago during a presidential election, I wanted to discuss voting and the fairness of results if voting is done by casting one single vote with more than 2 choices. ;; I believe that the single vote method is singularly unfair and unreliable when there are at least three choices if you are attempting to find the overall most acceptable choice rather than just the choice with the most first place votes.

As an example, well go through a voting exercies with 2 choices and then with 5 choices, and determine the winner in 2 different ways: one that simply counts first place votes, and two that actually takes into consideration a ranking structure to determine the winner based on overall most acceptable choice. ;; At first, well ask an invisible, pretend group of 100 make-believe people to choose between grape and cherry. ;; With 60 votes for cherry and 40 votes for grape, cherry is the winner - cherry received the most 1st place votes and is thus preferable. ;; Now, this doesnt tell you how preferable cherry is, by the way. ;; For example, what if in addition to preference they were asked to rank 1-10 how much they preferred the flavor over the other? ;; What if all the votes for cherry said they preferred cherry over grape at a level 10 - the highest, but all the votes for grape only preferred it over cherry at a level 2? ;; Does that skew the results? ;; Previously, it seemed that cherry just edged out grape. ;; But, the passion levels are so much higher with cherry that youd have to assume the results really mean that cherry is greatly preferred over grape. ;; If you went with grape, youd upset the cherry people to a much higher degree than the grape people with a cherry choice.  (Off Topic Side Note:  This reminds me of a Brian Regan bit:  "Grape!   ... or cherry!... theyre both favorites.  If they have grape, Ill get grape but if its cherry, itll be like - oh, thats ok cause theyre both favorites.  Theyre both FAVorites.")

OK, so now lets do this - we have a new vote, 100 people and they are asked to pick apples, bananas, pears, kumquats, or kiwis. ;; The votes come down like this:

• Apples - 30
• Bananas - 20
• Pears - 15
• Kumquats - 15
• Kiwis - 20

Making Apples the clear winner. ;; But, is this how people really feel? ;; When chatting with the imaginary group, I learn that some of them are very passionate one way or another about kiwis, but that emotions are spread more evenly about apples. ;; Bananas are kinda a middle of the road bunch (pardon the pun) while kumquats are hit or miss. ;; So, I decide to poll the same group, but this time I ask them to rank all 5 of the choices with "1" being their favorite down to "5" being the least favorite. ;; The first place votes are the same, but now we get back the results on the rest:

• Apples: 1-30, 2-10, 3-10, 4-25, 5-20
• Bananas: 1-20, 2-0, 3-50, 4-11, 5-19
• Pears: 1-15, 2-60, 3-25, 4-0, 5-0
• Kumquats: 1-15, 2-30, 3-10, 4-25, 5-20
• Kiwis: 1-20, 2-10, 3-0, 4-20, 5-25

Interesting - so what shall we do with this data? ;; Well, I decide to weight it - I give each first place vote 5 points, each second place vote 4 points, third place 3 points, fourth 2 points and fifth place votes get 1 point. ;; I add it up for each choice and divide the total by 100. ;; Wow! ;; The results are very different than when we just considered first place votes! ;; Why? ;; Well, were taking into consideration the weighted values of peoples feelings on the choices, not just the favorites. ;; If noone picked pears as first place but every single person picked them for second, wouldnt that be worth knowing? ;; Here are the weighted results from 1st place to 5th place:

• Pears - 3.90 / 5.00 (wouldve tied for 4th under original vote)
• Kumquats - 2.95 / 5.00 (wouldve tied for ;;4th under the original vote)
• Bananas - 2.91 / 5.00 (wouldve tied for 2nd under the original vote)
• Apples - 2.90 / 5.00 (wouldve won 1st place under the original vote)
• Kiwis - 2.05 / 5.00 (wouldve tied for 2nd under the original vote)

A very different picture when considering overall feelings for each choice. ;; Some people say that Bill Clinton would not have won against George Bush had it not been for Ross Perot "stealing votes". ;; I wonder what the results wouldve been if we voted by the ranking system? ;; Would the second place votes have mattered?

When the editor for the 2o2p magazine picks a winner of the current writing contest (http://www.2old2play.com/modules.php?name=News&file=article&sid=321&mode=&order=0&thold=0), will it be based solely on 1st place votes, or will a ranking system take place? ;; Even a 1st, 2nd, 3rd choice is a better ranking system than just 1st place votes, by the way - its preferable to rank the entire choice system (if you have 40 choices, you rank 1-40), but in the absence of a total rank, partial ranks are still more accurate than 1st place votes alone (think about the NCAA ranking system, if you will).

Or, we could just pick a number randomly out of a hat....