Rated pairwise preference ballot: Difference between revisions
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Certain minimum requirements for [[transitivity]] are apparent simply from looking at this table; for example, since the voter expressed a 50% difference in support for their 2nd choice>3rd choice, it wouldn't have made sense for them to express less than 50% support for their 1st choice>3rd choice. Another example is that, because they expressed 20% support for 1st>2nd, they must have had at least 20% support for 1st>3rd as well. To put it succinctly, for whatever degree of support a voter indicates in a given pairwise matchup cell, they must indicate at least that much support in all cells above, to the right, or to the upper-right of this cell. Thus, one way of collecting this pairwise information in a digital interface is to ask voters to start out by filling out the pairwise comparison between "Last choice>1st choice" (which is in the very bottom-left), and then accordingly allow the voter to fill out match-ups going up and/or right while imposing the required transitivity constraints. See [[Order theory#Strength of preference]] for further notes on transitivity in this framework.
Note that it doesn't make sense to allow a voter to indicate no preference between a higher-ranked candidate and a lower-ranked candidate, because then they'd essentially be putting them at the same rank. Thus, for ballot implementation purposes, a voter need only be given the ability to express some sort of positive preference in each matchup. Further, this only need start from the second-lowest allowed positive value, rather than the lowest; for example, if the voter is allowed to give support in increments of 10 (10% support, 20%, etc.), then because it must be assumed the voter gives at least the lowest positive value in a matchup (10%), only 20% and higher increments need to be offered as writable options for the voter.
== Connection to other ballot types ==
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