A few thought experiments. The median voter may be thought of as that hypothetical voter who would vote on the winning side of any question with two alternatives, based on the notion that voters and policies can probably be assigned geometric locations within some kind of "issue space." Can one speculate about the identity of the median voter, or the best fit for that label, given only cast rank ballots, and assuming no votes reverse any of the voters' pairwise preferences?
Details
Concept 1: Using only the cast relative preferences, try to draw a two-dimensional issue space that plots the voters and the candidates. Faint gray lines are
drawn through the middle voter on each axis, and the intersection of these lines can suggest a center of gravity, where a median voter might be expected, although it may
be that no voter is present there.
Since many results may be possible, four plots are generated. The inability to propose a single clear answer to this page's question is a major downside. The advantage
is that we can keep assumptions about unstated preferences to a minimum.
Concept 2: Build a majority by starting with a random voter, and continually adding in arguably "nearest" voters (to those already included) until a majority is attained. Do this many times, and then see how many times each voter was included in the majority. We might expect a "median voter" to be part of the majority all the time. A weakness of this approach is that we do not identify any specific positions that the majority could agree on. Note that, as I see it, the issue space premise would probably suggest that few voters are sincerely indifferent between any two candidates given as options. For this reason indifference of either or both of two factions on some pairwise contest is considered 0.5 points of distance, rather than finding that shared indifference constitutes a preference in common. Reversed preferences (e.g. A>B and B>A) count as one point of distance.
Concept 3: Considering propositions in decreasing order of the number of voters supporting them, successively exclude voters from the pool of possible median voters whenever they don't express this proposition. Additionally, if a proposition for some A>B can't be used, as no voters are left who express it, try weakening it to be the equality of A and B, so that at least B>A voters can be excluded. This process is close to Ranked Pairs, but identifying a voter instead of a candidate. The motivation here is that if more voters hold some position, it's more likely that the median voter holds it. This is particularly intuitive in the case of a stance held by a full majority, since any majority should include the median voter. A potential downside to this approach is the possibility that there exists, in some sense, a "better" proposal for the median voter, better supported by the evidence overall, that won't be found if voters are disqualified instantly upon evaluating a "strong" proposition that doesn't match their vote.
Concept 2: Build a majority by starting with a random voter, and continually adding in arguably "nearest" voters (to those already included) until a majority is attained. Do this many times, and then see how many times each voter was included in the majority. We might expect a "median voter" to be part of the majority all the time. A weakness of this approach is that we do not identify any specific positions that the majority could agree on. Note that, as I see it, the issue space premise would probably suggest that few voters are sincerely indifferent between any two candidates given as options. For this reason indifference of either or both of two factions on some pairwise contest is considered 0.5 points of distance, rather than finding that shared indifference constitutes a preference in common. Reversed preferences (e.g. A>B and B>A) count as one point of distance.
Concept 3: Considering propositions in decreasing order of the number of voters supporting them, successively exclude voters from the pool of possible median voters whenever they don't express this proposition. Additionally, if a proposition for some A>B can't be used, as no voters are left who express it, try weakening it to be the equality of A and B, so that at least B>A voters can be excluded. This process is close to Ranked Pairs, but identifying a voter instead of a candidate. The motivation here is that if more voters hold some position, it's more likely that the median voter holds it. This is particularly intuitive in the case of a stance held by a full majority, since any majority should include the median voter. A potential downside to this approach is the possibility that there exists, in some sense, a "better" proposal for the median voter, better supported by the evidence overall, that won't be found if voters are disqualified instantly upon evaluating a "strong" proposition that doesn't match their vote.
Instructions
Enter your ballots like this, one per line:
456: Alice>Bob=Carl>Debra
The number represents the size of the voting bloc. Decimals are OK. The size can also be left off and it will then be randomized.
Candidate names can contain spaces. Each candidate in the list should be separated by > or =. Pipes (i.e. |) and any series of > will be interpreted as single >s. Not every candidate needs to be listed; candidates present on the ballots but missing from one faction's ranking will be interpreted as ranked tied for last, below any explicitly ranked candidates.
Click submit to generate an analysis.
456: Alice>Bob=Carl>Debra
The number represents the size of the voting bloc. Decimals are OK. The size can also be left off and it will then be randomized.
Candidate names can contain spaces. Each candidate in the list should be separated by > or =. Pipes (i.e. |) and any series of > will be interpreted as single >s. Not every candidate needs to be listed; candidates present on the ballots but missing from one faction's ranking will be interpreted as ranked tied for last, below any explicitly ranked candidates.
Click submit to generate an analysis.
|
Enter the ballots for an election:
|
||
| Enable image generation (slower) |