Pairwise counting: Difference between revisions
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{{Tenn_voting_example}} |
{{Tenn_voting_example}} |
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As these ballot preferences are converted into pairwise counts they can be entered into a table. |
As these ballot preferences are converted into pairwise counts they can be entered into a table. |
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The following square-grid table uses the popularity sequence calculated by the [[Kemeny-Young Maximum Likelihood Method|Condorcet-Kemeny method]], which does calculations that ensure that the sum of the pairwise counts in the upper-right triangular area cannot be increased by changing the sequence of the candidates. |
The following square-grid table uses the popularity sequence calculated by the [[Kemeny-Young Maximum Likelihood Method|Condorcet-Kemeny method]], which does calculations that ensure that the sum of the pairwise counts in the upper-right triangular area cannot be increased by changing the sequence of the candidates. |
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{| class="wikitable" |
{| class="wikitable" |
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The following tally table shows another table arrangement. |
The following tally table shows another table arrangement. |
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{| class="wikitable" |
{| class="wikitable" |
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|+Tally table |
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! rowspan=2" | All possible pairs<br/>of choice names |
! rowspan="2"" | All possible pairs<br />of choice names |
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! colspan=3 | Number of votes with indicated preference |
! colspan="3" | Number of votes with indicated preference |
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! style="text-align:left" | Prefer X over Y |
! style="text-align:left" | Prefer X over Y |
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! style="text-align:left" | Prefer Y over X |
! style="text-align:left" | Prefer Y over X |
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| align="left" | X = Memphis<br/>Y = Nashville |
| align="left" | X = Memphis<br />Y = Nashville |
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| align="left" | 42% |
| align="left" | 42% |
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| align="left" | 0 |
| align="left" | 0 |
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| align="left" | 58% |
| align="left" | 58% |
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| align="left" | X = Memphis<br/>Y = Chattanooga |
| align="left" | X = Memphis<br />Y = Chattanooga |
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| align="left" | 42% |
| align="left" | 42% |
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| align="left" | 0 |
| align="left" | 0 |
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| align="left" | 58% |
| align="left" | 58% |
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| align="left" | X = Memphis<br/>Y = Knoxville |
| align="left" | X = Memphis<br />Y = Knoxville |
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| align="left" | 42% |
| align="left" | 42% |
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| align="left" | 0 |
| align="left" | 0 |
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| align="left" | 58% |
| align="left" | 58% |
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| align="left" | X = Nashville<br/>Y = Chattanooga |
| align="left" | X = Nashville<br />Y = Chattanooga |
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| align="left" | 68% |
| align="left" | 68% |
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| align="left" | 0 |
| align="left" | 0 |
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| align="left" | 32% |
| align="left" | 32% |
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| align="left" | X = Nashville<br/>Y = Knoxville |
| align="left" | X = Nashville<br />Y = Knoxville |
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| align="left" | 68% |
| align="left" | 68% |
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| align="left" | 0 |
| align="left" | 0 |
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| align="left" | 32% |
| align="left" | 32% |
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| align="left" | X = Chattanooga<br/>Y = Knoxville |
| align="left" | X = Chattanooga<br />Y = Knoxville |
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| align="left" | 83% |
| align="left" | 83% |
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| align="left" | 0 |
| align="left" | 0 |
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