Democracy Center - When is the result of sequential choice voting conclusive?

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Research and advice on methods of voting and election

In Democracy with Sequential Choice and Fund Voting there is an example of sequential choice which proved beyond any doubt that the difference in the number of votes for some of the choices relating to the subject (article II.A.5. Collective responsibility: Sequential choice as a means of sounding out) was negligible. The fact that this was conclusive definitely facilitated any further processing of the issue.

Thus one can ask, when is there a conclusive difference between the two alternatives that receive the highest number of points. In the Gjábakki sequential choice project the number of points received by the two top alternatives was 4,039 and 2,498, respectively. To find out whether the difference is conclusive the following reasoning may be employed:

The total number of votes was 1,351. As there were five alternatives, each vote yielded 10 points, i.e. there were 13,510 points in all.

Should one of the road placements be assigned position 1 by all voters, which assigns 4 points to it, that road placement receives 5,404 points.

Should one of the road placements be assigned position 2 by all voters, which assigns 3 points to it, that road placement receives 4,053 points.

The difference between these two road placements is 1,351 points, but the difference between road placements 1 and 2 was, in fact, 1,541 points, which must be regarded as a conclusive difference.

Furthermore, it can be found out algebraically to what extent the difference between the two top alternatives is conclusive:

y is the number of points denoting the difference between two positions

x is the total number of votes

n is the number of alternatives

x rank A first

A receives (n–1)x points

x rank B second

B receives (n-–2)x points

y=(n–1)x–(n–2)x=nx–x–nx+2x=x

y=x

 

Consequently, x is the number of points denoting a clear difference between the positions.