Sample Results that Demonstrate Fairness

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VoteFair Ranking Results calculated at  www.VoteFair.org  2005-July-4  13:29


Election title:

     Example in which traditional (plurality and runoff) voting gives unfair results     

Question (number 1) title:

     Sample Election     



The most preferred and most representative choice is:

    Farah

Overall popularity ranking:

     
Popularity Choice Graphic summary of tally information
(details in mouse-over ALT text)
First -most popular Farah 65 voters prefer Farah over Gordon0 voters have an equal preference for Farah and Gordon35 voters prefer Gordon over Farah 60 voters prefer Farah over Clifford0 voters have an equal preference for Farah and Clifford40 voters prefer Clifford over Farah
Second -most popular Gordon The percent bars above indicate comparisons with the choice to the left 60 voters prefer Gordon over Clifford0 voters have an equal preference for Gordon and Clifford40 voters prefer Clifford over Gordon
Third -most popular Clifford The percent bars above indicate comparisons with the choice to the left



VoteFair Representation Ranking

  
First -most representative choice is: Farah
Second -most representative choice is: Clifford
Third -most representative choice is: Gordon

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 ranking results be used? When a second candidate is elected to a second equivalent seat on a board of directors, or when an organization pursues a second activity in addition to the most popular activity.


Comparison of VoteFair Ranking with other voting methods

  
Voting method Winner
VoteFair Farah
Instant runoff Tie between:
    Clifford
    Gordon
(100 ballots at least partially ignored because they include an equal preference at a significant step in the runoff process.)
(Choice eliminated in the first round: Farah)
Majority None of the choices has won a majority ( more than half ) the votes.
Plurality Clifford
Condorcet Farah
Borda count Farah

Details of plurality results
  
Choice Vote count Percentage Percentage bar
Clifford 40 40 40 voters marked Clifford as their first choice
Gordon 35 35 35 voters marked Gordon as their first choice
Farah 25 25 25 voters marked Farah as their first 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: 100
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 = Farah
Y = Gordon 		65
65 voters prefer Farah over Gordon 		0
0 voters have an equal preference for Farah and Gordon 		35
35 voters prefer Gordon over Farah
X = Farah
Y = Clifford 		60
60 voters prefer Farah over Clifford 		0
0 voters have an equal preference for Farah and Clifford 		40
40 voters prefer Clifford over Farah
X = Gordon
Y = Clifford 		60
60 voters prefer Gordon over Clifford 		0
0 voters have an equal preference for Gordon and Clifford 		40
40 voters prefer Clifford over Gordon
The highest score (which equals the sum of the bold underlined numbers, plus either tally number in any tied pair of choices) is: 185
Number of all possible valid sequences (without ties): 6
First sequence:
  1. Clifford
  2. Gordon
  3. Farah
Last sequence:
  1. Farah
  2. Gordon
  3. Clifford
© Copyright 2005 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.)

  • 1,3,2 x40
  • 2,3,1 x35
  • 3,2,1 x25

© Copyright 2005 Solutions Through Innovation at www.VoteFair.org

Software version: 2005-June-28

The free VoteFair ranking service is subsidized by sales of The Creative Problem Solver's Toolbox : A Complete Course in the Art of Creating Solutions to Problems of Any Kind , which was written by Richard Fobes, the inventor of VoteFair ranking and the programmer and writer for the VoteFair site. Cover of The Creative Problem Solver's Toolbox


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