STAR voting: Difference between revisions
→Precinct summability
Line 204:
|'''9 points'''
|}
As can be seen above, the number of points for each candidate can be added up (i.e. 10 + 3 = 13 points for White) and the number of votes for each candidate in each head-to-head matchup can be added up (i.e. 3 + 2 = 5 votes for Dark>Milk), allowing us to see all of the final relevant preference information when everything is added up. All of the precincts' matrices can be combined in this manner until a final matrix is reached. If the matrix is organized such that it is in descending order of points (i.e. higher-scored candidates go in higher rows), then the winner can be determined simply by, so long as there are no scorewise ties (ties on points) between the top two candidates and anyone else, looking at the top two rows and looking for the result in the head-to-head matchup between them.
So, for example, if the above matrix was the final matrix, then we can find the result as follows:
{| class="wikitable"
|+
!
!<big><u>Dark</u></big>
!<s><big>White</big></s>
!<small>Milk</small>
!<small>Almond</small>
|-
|'''<big><u>Dark</u></big>'''
|''16 points''
|'''<u>3 (+1 Win)</u>'''
|<small>5 (+5 Win)</small>
|<small>5 (+5 Win)</small>
|-
|<s><big>White</big></s>
|'''<small>2 (-1 Loss)</small>'''
|''13 points''
|<small>2 (-1 Loss)</small>
|<small>2 (-1 Loss)</small>
|-
|<small>Milk</small>
|<small>0 (-5 Loss)</small>
|<small>3 (+1 Win)</small>
|<small>9 points</small>
|<small>0 (Tie)</small>
|-
|<small>Almond</small>
|<small>0 (-5 Loss)</small>
|<small>3 (+1 Win)</small>
|<small>0 (Tie)</small>
|<small>9 points</small>
|}
As can be seen after sorting the candidates by points, Dark and White would go to the automatic runoff because they have more points than any other candidates, and then Dark would win, because Dark has 1 more vote than (is preferred/scored higher by 1 more voter than) White in their head-to-head matchup.
(Note that precinct-summability becomes more complex when dealing with write-in candidates. See [[Pairwise counting#Notes]] for ideas on how to deal with this; essentially, the most comprehensive way is to count the number of voters who score a candidate, filling in that number of votes preferring that candidate above each other candidate in a head-to-head matchup, and subtract a vote from each head-to-head matchup where the voter scored another candidate above or equal to the scored candidate. Since write-ins so rarely win, in practice, it is possible to simply record how many voters scored the write-in and what score they gave that candidate, and only do a second round of tallying in the rare case that the write-in makes it to the automatic runoff. If it is predicted that the write-in may garner significant support, then the election officials can be told to record this candidate's head-to-head matchups as well.)
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