minkowskiDistanceSets: minkowskiDistanceSets

In robiRagan/voteR: Spatial Voting Models in R

Description

Calculates the sailence weighted Minkowski distance between all combinations of a set of voters and a set of alternatives in an n-dimensional space.

Usage

minkowskiDistanceSets(
  idealsMatrix,
  altsMatrix,
  minkoOrderVector,
  salienceMatrix
)

Arguments

idealsMatrix	A numberVoters x numberDimensions matrix of numerics. Each row is a voter and each column is a dimension in the policy space, <d1,d2,...dn>. The values in a given row give the location of one voters ideal point, the point that is the argMax of their utility function.Example: In a two dimensional space the if entry in the matrix at location (v=2,d1=2,d=2) is <.5,.5> then the peak of voter 2's utility function in the two dimensional issue space is at .5,.5.
altsMatrix	A numberAlts x numberDimensions matrix of numerics. Each row is an alternative and each column is a dimension in the policy space, <d1,d2,...dn>. The values in a given row give the location of that alternative in the policy space. Example: In a two dimensional space the if entry in the matrix at location (d=2,d1=2,d=2) is <.25,.75> then the location of that alternative in the two dimensional issue space is at .25,.75.
minkoOrderVector	A numVoters length vector of doubles. It is the “order" of the Minkowski Distance being used. In this packge it should be an element of [1,100]. Examples for cases where the salience on all dimensions is equal: 1 = Manhattan Distance. diamond shaped indifference curves, perfect substitutes. 2 = Euclidian Distance. If salience on all dimensions is equal, circular indifference curves. 100 = Aproximates Chebyshev Distance. If salience on all dimensions is equal square indifference curves, perfect compliments.
salienceMatrix	A matrix of doubles that is numberOfDimensions long: <sd1, sd2, sd3, ... sdk>. Each element of the vector represents the *relative* saliance of each dimension for a voter. The dimension with the lowest salience serves as the "numeraire" dimension and should recieve a salience of 1. All the other saliences are expressed in units of this "numeraire". So if a dimension is twice as important to a voter as the numeraire dimension it recieves a salience of 2. Example: The second row is 1 2 3. This means that for voter two (second row) the salience of dimension 1 is the numeraire, dimension 2 is twice as saient as dimension 1 and dimension 3 is three times as salient as dimension one.

Details

This function will find the salience weighted Minkowski Distance for a set of voters whose ideal points are stacked in a numberVoters x numberDimensions matrix and a set of alternatives that are stacked into a numberAlternatives x numberDimensions matrix. Each voter can have a different 'order' for their Minkowski Distance and a set of 'sailence' weights for each policy dimension.

Value

distMatrix A numVoters x numAlts matrix that contains the Minkowski Distance between each voter and each alternative, given a voter's salience and Minkowski order. The sailence and the Minkowski order together determine a voter's utility function.

See Also

Other minkowski: minkowskiDistancePairOfPoints(), minkowskiUtilitySets(), prefOrderMinko()

Other utility functions: minkowskiDistancePairOfPoints(), minkowskiUtilitySets(), prefOrderMinko()

robiRagan/voteR documentation built on Feb. 27, 2020, 6:48 p.m.