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VoteFair Ranking Results calculated at  www.VoteFair.org 2006-July-21  0:06

Poll title:

     VoteFair poll for So You Think You Can Dance, Top 10    

Question (number 1) title:

     How well can these dancers dance?    

The following choices are tied as the most preferred and most representative:

    (tie) Allison

    (tie) Benji

About ties: The presence of a tie among choices indicates that the number of voters who express a preference one way exactly equal the number of voters who express the opposite preference. If a tie occurs, look at the numbers in the tally table (below) to confirm this exact balance.

Overall popularity ranking:

     
Popularity Choice VoteFair
ranking
score		 Traditional
vote count
(for comparison)
First-most popular
is a tie among these choices		 Allison Ranking score is 67 for Allison
Benji Ranking score is 65 for Benji
Second-most popular Heidi Ranking score is 46 for Heidi
Third-most popular Travis Ranking score is 45 for Travis
Fourth-most popular
is a tie among these choices		 Donyelle Ranking score is 28 for Donyelle
Ivan Ranking score is 30 for Ivan
Fifth-most popular Natalie Ranking score is 21 for Natalie
Sixth-most popular
is a tie among these choices		 Dimitri Ranking score is 6 for Dimitri
Ryan Ranking score is 5 for Ryan
Seventh-most popular Martha Ranking score is 0 for Martha

VoteFair representation Ranking

  
First-most representative choice
is a tie among these choices:		 Allison
Benji

Additional levels of representation
cannot be determined until the above tie
has been resolved, which can be done
by introducing a tie-breaking vote.

VoteFair representation ranking results should be used when more than one choice is to be selected. Why? When there are 100 voters, 51 of them can choose the first winner, so the other 49 voters deserve extra influence in choosing the second winner (instead of letting the 51 voters also choose the second winner). When should representation results be used? When a second candidate is elected to a second equivalent seat in a state legislature, or when an organization pursues a simultaneous second activity in addition to the most popular activity.

Comparison of VoteFair Ranking with other voting methods

  
Voting method Winner
VoteFair Tie between:
    Allison
    Benji
Instant runoff Tie between:
    Allison
    Benji
(The runoff steps did not involve a single choice being eliminated in the first round.)
Majority None of the choices has won a majority ( more than half ) the votes.

(3 ballots ignored because they rank more than one choice as the most-preferred choice.)
Plurality Tie between:
    Allison
    Benji

(3 ballots ignored because they rank more than one choice as the most-preferred choice.)
Condorcet Tie between:
    Allison
    Benji
Borda count Benji

(10 ballots ignored because they rank more than one choice at the same preference level.)

Details of plurality results

  
Choice Vote count Percentage
Benji 6 26
Allison 6 26
Dimitri 3 13
Travis 2 9
Ivan 2 9
Heidi 2 9
Donyelle 2 9
Ryan 0 0
Natalie 0 0
Martha 0 0
(3 ballots ignored in plurality counting because they rank more than one choice as the most-preferred choice.)

Notice that the choice with the most plurality votes is not necessarily the most popular. Similarly the choice with the fewest plurality votes is not necessarily the least popular.

Data and Calculation Summary
Number of votes: 26
The following tally table summarizes all the preferences of all the voters. The bold underlined numbers are the ones that apply to the winning sequence.
  
All possible pairs of choice names Number of votes with indicated preference
Prefer X over Y Equal preference Prefer Y over X
X = Allison
Y = Benji		 13
13 voters prefer Allison over Benji		 0
0 voters have an equal preference for Allison and Benji		 13
13 voters prefer Benji over Allison
X = Allison
Y = Heidi		 18
18 voters prefer Allison over Heidi		 2
2 voters have an equal preference for Allison and Heidi		 6
6 voters prefer Heidi over Allison
X = Allison
Y = Travis		 16
16 voters prefer Allison over Travis		 0
0 voters have an equal preference for Allison and Travis		 10
10 voters prefer Travis over Allison
X = Allison
Y = Donyelle		 16
16 voters prefer Allison over Donyelle		 1
1 voter has an equal preference for Allison and Donyelle		 9
9 voters prefer Donyelle over Allison
X = Allison
Y = Ivan		 19
19 voters prefer Allison over Ivan		 2
2 voters have an equal preference for Allison and Ivan		 5
5 voters prefer Ivan over Allison
X = Allison
Y = Natalie		 22
22 voters prefer Allison over Natalie		 0
0 voters have an equal preference for Allison and Natalie		 4
4 voters prefer Natalie over Allison
X = Allison
Y = Dimitri		 18
18 voters prefer Allison over Dimitri		 3
3 voters have an equal preference for Allison and Dimitri		 5
5 voters prefer Dimitri over Allison
X = Allison
Y = Ryan		 23
23 voters prefer Allison over Ryan		 0
0 voters have an equal preference for Allison and Ryan		 3
3 voters prefer Ryan over Allison
X = Allison
Y = Martha		 24
24 voters prefer Allison over Martha		 0
0 voters have an equal preference for Allison and Martha		 2
2 voters prefer Martha over Allison
X = Benji
Y = Heidi		 18
18 voters prefer Benji over Heidi		 3
3 voters have an equal preference for Benji and Heidi		 5
5 voters prefer Heidi over Benji
X = Benji
Y = Travis		 17
17 voters prefer Benji over Travis		 1
1 voter has an equal preference for Benji and Travis		 8
8 voters prefer Travis over Benji
X = Benji
Y = Donyelle		 16
16 voters prefer Benji over Donyelle		 3
3 voters have an equal preference for Benji and Donyelle		 7
7 voters prefer Donyelle over Benji
X = Benji
Y = Ivan		 19
19 voters prefer Benji over Ivan		 0
0 voters have an equal preference for Benji and Ivan		 7
7 voters prefer Ivan over Benji
X = Benji
Y = Natalie		 21
21 voter prefers Benji over Natalie		 0
0 voters have an equal preference for Benji and Natalie		 5
5 voters prefer Natalie over Benji
X = Benji
Y = Dimitri		 20
20 voters prefer Benji over Dimitri		 1
1 voter has an equal preference for Benji and Dimitri		 5
5 voters prefer Dimitri over Benji
X = Benji
Y = Ryan		 20
20 voters prefer Benji over Ryan		 0
0 voters have an equal preference for Benji and Ryan		 6
6 voters prefer Ryan over Benji
X = Benji
Y = Martha		 21
21 voter prefers Benji over Martha		 2
2 voters have an equal preference for Benji and Martha		 3
3 voters prefer Martha over Benji
X = Heidi
Y = Travis		 12
12 voters prefer Heidi over Travis		 3
3 voters have an equal preference for Heidi and Travis		 11
11 voter prefers Travis over Heidi
X = Heidi
Y = Donyelle		 11
11 voter prefers Heidi over Donyelle		 4
4 voters have an equal preference for Heidi and Donyelle		 11
11 voter prefers Donyelle over Heidi
X = Heidi
Y = Ivan		 16
16 voters prefer Heidi over Ivan		 1
1 voter has an equal preference for Heidi and Ivan		 9
9 voters prefer Ivan over Heidi
X = Heidi
Y = Natalie		 16
16 voters prefer Heidi over Natalie		 1
1 voter has an equal preference for Heidi and Natalie		 9
9 voters prefer Natalie over Heidi
X = Heidi
Y = Dimitri		 17
17 voters prefer Heidi over Dimitri		 3
3 voters have an equal preference for Heidi and Dimitri		 6
6 voters prefer Dimitri over Heidi
X = Heidi
Y = Ryan		 19
19 voters prefer Heidi over Ryan		 1
1 voter has an equal preference for Heidi and Ryan		 6
6 voters prefer Ryan over Heidi
X = Heidi
Y = Martha		 17
17 voters prefer Heidi over Martha		 3
3 voters have an equal preference for Heidi and Martha		 6
6 voters prefer Martha over Heidi
X = Travis
Y = Donyelle		 14
14 voters prefer Travis over Donyelle		 1
1 voter has an equal preference for Travis and Donyelle		 11
11 voter prefers Donyelle over Travis
X = Travis
Y = Ivan		 15
15 voters prefer Travis over Ivan		 0
0 voters have an equal preference for Travis and Ivan		 11
11 voter prefers Ivan over Travis
X = Travis
Y = Natalie		 18
18 voters prefer Travis over Natalie		 0
0 voters have an equal preference for Travis and Natalie		 8
8 voters prefer Natalie over Travis
X = Travis
Y = Dimitri		 19
19 voters prefer Travis over Dimitri		 1
1 voter has an equal preference for Travis and Dimitri		 6
6 voters prefer Dimitri over Travis
X = Travis
Y = Ryan		 22
22 voters prefer Travis over Ryan		 0
0 voters have an equal preference for Travis and Ryan		 4
4 voters prefer Ryan over Travis
X = Travis
Y = Martha		 18
18 voters prefer Travis over Martha		 2
2 voters have an equal preference for Travis and Martha		 6
6 voters prefer Martha over Travis
X = Donyelle
Y = Ivan		 13
13 voters prefer Donyelle over Ivan		 0
0 voters have an equal preference for Donyelle and Ivan		 13
13 voters prefer Ivan over Donyelle
X = Donyelle
Y = Natalie		 16
16 voters prefer Donyelle over Natalie		 0
0 voters have an equal preference for Donyelle and Natalie		 10
10 voters prefer Natalie over Donyelle
X = Donyelle
Y = Dimitri		 16
16 voters prefer Donyelle over Dimitri		 2
2 voters have an equal preference for Donyelle and Dimitri		 8
8 voters prefer Dimitri over Donyelle
X = Donyelle
Y = Ryan		 17
17 voters prefer Donyelle over Ryan		 1
1 voter has an equal preference for Donyelle and Ryan		 8
8 voters prefer Ryan over Donyelle
X = Donyelle
Y = Martha		 16
16 voters prefer Donyelle over Martha		 2
2 voters have an equal preference for Donyelle and Martha		 8
8 voters prefer Martha over Donyelle
X = Ivan
Y = Natalie		 13
13 voters prefer Ivan over Natalie		 3
3 voters have an equal preference for Ivan and Natalie		 10
10 voters prefer Natalie over Ivan
X = Ivan
Y = Dimitri		 14
14 voters prefer Ivan over Dimitri		 2
2 voters have an equal preference for Ivan and Dimitri		 10
10 voters prefer Dimitri over Ivan
X = Ivan
Y = Ryan		 20
20 voters prefer Ivan over Ryan		 1
1 voter has an equal preference for Ivan and Ryan		 5
5 voters prefer Ryan over Ivan
X = Ivan
Y = Martha		 23
23 voters prefer Ivan over Martha		 1
1 voter has an equal preference for Ivan and Martha		 2
2 voters prefer Martha over Ivan
X = Natalie
Y = Dimitri		 15
15 voters prefer Natalie over Dimitri		 1
1 voter has an equal preference for Natalie and Dimitri		 10
10 voters prefer Dimitri over Natalie
X = Natalie
Y = Ryan		 17
17 voters prefer Natalie over Ryan		 3
3 voters have an equal preference for Natalie and Ryan		 6
6 voters prefer Ryan over Natalie
X = Natalie
Y = Martha		 16
16 voters prefer Natalie over Martha		 4
4 voters have an equal preference for Natalie and Martha		 6
6 voters prefer Martha over Natalie
X = Dimitri
Y = Ryan		 12
12 voters prefer Dimitri over Ryan		 2
2 voters have an equal preference for Dimitri and Ryan		 12
12 voters prefer Ryan over Dimitri
X = Dimitri
Y = Martha		 15
15 voters prefer Dimitri over Martha		 2
2 voters have an equal preference for Dimitri and Martha		 9
9 voters prefer Martha over Dimitri
X = Ryan
Y = Martha		 12
12 voters prefer Ryan over Martha		 4
4 voters have an equal preference for Ryan and Martha		 10
10 voters prefer Martha over Ryan
The highest score (which equals the sum of the bold underlined numbers, plus either tally number in any tied pair of choices) is: 770
Number of all possible valid sequences (without ties): 3,628,800
First sequence:
  1. Allison
  2. Donyelle
  3. Heidi
  4. Martha
  5. Natalie
  6. Benji
  7. Dimitri
  8. Ivan
  9. Ryan
  10. Travis
Last sequence:
  1. Travis
  2. Ryan
  3. Ivan
  4. Dimitri
  5. Benji
  6. Natalie
  7. Martha
  8. Heidi
  9. Donyelle
  10. Allison
© Copyright 2006 Solutions Through Innovation at www.VoteFair.org

Detailed ballot information
(The numbers indicate the choices
as listed in "First sequence" above,
a comma indicates the next lower preference level,
"&" joins choices at the same preference level,
and "x" precedes the vote count.)

  • 1&8,6,10,4&5,2&3,7&9 x1
  • 1,3,10,5,9,8,4,2,6,7 x1
  • 1,5,3,8,10,9,7,4,2,6 x1
  • 1,5,8,9,2&3&4&6&7&10 x1
  • 1,6,10,2,3,8,5,7,4,9 x1
  • 1,6,10,3,7,8,2,4,5,9 x1
  • 1,6,8,4,3&10,9,5,2,7 x1
  • 10,2,1,6,5,8,9,4,7,3 x1
  • 10,6,1,2,3&4&5&7&8&9 x1
  • 2&6,3&10,5&8,1&7,4&9 x1
  • 2&9,3&6,1&7,5&8,4&10 x1
  • 2,6,1&3,5,7,8,10,9,4 x1
  • 2,6,8,1,4,5,3,10,9,7 x1
  • 3,1,10,6,4&5&9,7&8,2 x1
  • 3,10,6,7,5,8,1,9,4,2 x1
  • 6,1,2,10,7,8,3,9,5,4 x1
  • 6,1,3,2,10,5,7,8,4,9 x1
  • 6,1,3,7,2,10,4,8,5,9 x1
  • 6,10,2,1,3,5,9,8,7,4 x1
  • 6,2,10,3,1,8,7,5,9,4 x1
  • 6,3,10,2,1,9,8,5,4,7 x1
  • 7,1&8,9,5,2&3&4&6,10 x1
  • 7,1,6,3,8,4,2,5,10,9 x1
  • 7,10,1,6,5,3,8,2,4,9 x1
  • 8,4&5&9,10,1&2&3&7,6 x1
  • 8,6,2,4,10,9,7,5,1,3 x1

© Copyright 2006 Solutions Through Innovation at www.VoteFair.org

Software version: 2006-June-30

The free VoteFair ranking service is subsidized by sales of Ending The Hidden Unfairness In U.S. Elections and The Creative Problem Solver's Toolbox, which were written by Richard Fobes, the inventor of VoteFair ranking and the programmer and writer for the VoteFair site. Cover of Ending The Hidden Unfairness In U.S. Elections Cover of The Creative Problem Solver's Toolbox

 

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