Majority Judgment: Difference between revisions
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(→Example application: Updated following Wikipeia) |
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If there were four ratings named "Excellent", "Good", "Fair", and "Poor", and each voter assigned four different ratings to the four cities, then the sorted scores would be as follows: |
If there were four ratings named "Excellent", "Good", "Fair", and "Poor", and each voter assigned four different ratings to the four cities, then the sorted scores would be as follows: |
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<table> |
<table> |
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<td align=right>City</td> |
<td align=right>City </td> |
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<td> |
<td> |
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<table cellpadding=0 width= |
<table cellpadding=0 width=500 border=0 cellspacing=0> |
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<tr> |
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<td width=49%> </td> |
<td width=49%> </td> |
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<td width=2% textalign=center> |
<td width=2% textalign=center>↓</td> |
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<td width=49%>Median point</td> |
<td width=49%>Median point</td> |
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</tr> |
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<td align=right>Nashville</td> |
<td align=right>Nashville</td> |
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<td> |
<td> |
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<table cellpadding=0 width= |
<table cellpadding=0 width=500 border=0 cellspacing=0> |
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<tr> |
<tr> |
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<td bgcolor=green width=26%> </td> |
<td bgcolor=green width=26%> </td> |
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<td bgcolor=YellowGreen width=42%></td> |
<td bgcolor=YellowGreen width=42%></td> |
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<td bgcolor=Gold width=32%></td> |
<td bgcolor=Gold width=32%></td> |
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<td bgcolor=red width=0%></td> |
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</tr> |
</tr> |
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</table> |
</table> |
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<td align=right>Chattanooga</td> |
<td align=right>Chattanooga</td> |
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<td> |
<td> |
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<table cellpadding=0 width= |
<table cellpadding=0 width=500 border=0 cellspacing=0> |
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<tr> |
<tr> |
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<td bgcolor=green width=15%> </td> |
<td bgcolor=green width=15%> </td> |
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<td bgcolor=YellowGreen width=43%></td> |
<td bgcolor=YellowGreen width=43%></td> |
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<td bgcolor=Gold width=42%></td> |
<td bgcolor=Gold width=42%></td> |
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<td bgcolor=red width=0%></td> |
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</tr> |
</tr> |
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</table> |
</table> |
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<td align=right>Knoxville</td> |
<td align=right>Knoxville</td> |
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<td> |
<td> |
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<table cellpadding=0 width= |
<table cellpadding=0 width=500 border=0 cellspacing=0> |
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<tr> |
<tr> |
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<td bgcolor=green width=17%> </td> |
<td bgcolor=green width=17%> </td> |
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<td bgcolor=YellowGreen width=15%></td> |
<td bgcolor=YellowGreen width=15%></td> |
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<td bgcolor=Gold width=26%></td> |
<td bgcolor=Gold width=26%></td> |
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<td bgcolor= |
<td bgcolor=DarkOrange width=42%></td> |
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</tr> |
</tr> |
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</table> |
</table> |
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<td align=right>Memphis</td> |
<td align=right>Memphis</td> |
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<td> |
<td> |
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<table cellpadding=0 width= |
<table cellpadding=0 width=500 border=0 cellspacing=0> |
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<tr> |
<tr> |
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<td bgcolor=green width=42%> </td> |
<td bgcolor=green width=42%> </td> |
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<td bgcolor= |
<td bgcolor=DarkOrange width=58%></td> |
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<td bgcolor=Gold width=0%></td> |
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<td bgcolor=red width=58%></td> |
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</tr> |
</tr> |
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</table> |
</table> |
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<td> </td> |
<td> </td> |
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<td> |
<td> |
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<table cellpadding=1 |
<table cellpadding=1 border=0 cellspacing=1> |
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<tr> |
<tr> |
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<td |
<td> </td> |
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<td bgcolor=green> </td> |
<td bgcolor=green> </td> |
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<td> |
<td> Excellent </td> |
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<td bgcolor=YellowGreen> </td> |
<td bgcolor=YellowGreen> </td> |
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<td> Good </td> |
<td> Good </td> |
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<td bgcolor=Gold> </td> |
<td bgcolor=Gold> </td> |
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<td> Fair </td> |
<td> Fair </td> |
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<td bgcolor= |
<td bgcolor=DarkOrange> </td> |
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<td> Poor </td> |
<td> Poor </td> |
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<td width=50%> </td> |
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</tr> |
</tr> |
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</table> |
</table> |
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</table> |
</table> |
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The |
The median rating for Nashville and Chatanooga is "Good"; for Knoxville, "Fair"; and for Memphis, "Poor". Nashville and Chatanooga are tied, so "Good" ratings have to be removed from both, until their medians become different. After removing 16% "Good" ratings from the votes of each, the sorted ratings are now: |
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<table> |
<table> |
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<tr> |
<tr> |
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<td align=right>City</td> |
<td align=right>City </td> |
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<td> |
<td> |
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<table cellpadding=0 width= |
<table cellpadding=0 width=500 border=0 cellspacing=0> |
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<tr> |
<tr> |
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<td width=49%> </td> |
<td width=49%> </td> |
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<td width=2% textalign=center> |
<td width=2% textalign=center>↓</td> |
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<td width=49%>Median point</td> |
<td width=49%>Median point</td> |
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</tr> |
</tr> |
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<td align=right>Nashville</td> |
<td align=right>Nashville</td> |
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<td> |
<td> |
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<table cellpadding=0 width= |
<table cellpadding=0 width=500 border=0 cellspacing=0> |
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<tr> |
<tr> |
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<td bgcolor=gray width=8%> </td> |
<td bgcolor=gray width=8%> </td> |
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<td align=right>Chattanooga</td> |
<td align=right>Chattanooga</td> |
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<td> |
<td> |
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<table cellpadding=0 width= |
<table cellpadding=0 width=500 border=0 cellspacing=0> |
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<tr> |
<tr> |
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<td bgcolor=gray width=8%></td> |
<td bgcolor=gray width=8%></td> |
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<td> </td> |
<td> </td> |
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<td> |
<td> |
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<table cellpadding=1 |
<table cellpadding=1 border=0 cellspacing=1> |
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<tr> |
<tr> |
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<td |
<td> </td> |
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<td bgcolor=gray> </td> |
<td bgcolor=gray> </td> |
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<td> Removed ratings (sorted to both ends evenly for easy comparison of medians with above).</td> |
<td> Removed ratings (sorted to both ends evenly for easy comparison of medians with above).</td> |
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<td width=20%> </td> |
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</tr> |
</tr> |
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</table> |
</table> |
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</td> |
</td> |
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</table> |
</table> |
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Chatanooga now has the same number of "Fair" ratings as "Good" and "Excellent" combined, so its median is rounded down to "Fair", while Nashville's median remains at "Good"<ref>After removal, Chatanooga has 42% of the initial electorate at "Fair", 27% "Good", and 15% "Excellent", while Nashville has 32% "Fair", 26% "Good", and 26% "Excellent"</ref> and so '''Nashville''', the capital in real life, wins. |
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If voters from Knoxville and Chattanooga were to rate Nashville as "Poor" and/or both sets of voters were to rate Chattanooga as "Excellent", in an attempt to make their preferred candidate Chatanooga win, the winner would still be Nashville. |
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==See also== |
==See also== |
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