minkowskiUtilitySets: minkowskiUtilitySets
In robiRagan/voteR: Spatial Voting Models in R

Description Usage Arguments Details Value See Also

Calculates the sailence weighted Minkowski utility for a set of voters and a set of alternatives in an 2-dimensional space.

minkowskiUtilitySets(
  idealsMatrix,
  altsMatrix,
  minkoOrderVector,
  lossOrderVector,
  salienceMatrix
)

`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 lengh 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.
`lossOrderVector`	A numVoters lengh vector of doubles. It is the “order" of the loss function being used. In short the Minkowski Distance is the way that a voter percieves the distance between their ideal point and another alternative. The loss function tells us how that distance is converted into utility for the voter. If lossOrderVector=1, then the voter has linear loss and their disutility for an alternative is equal to the minkowski distance. If lossOrderVector=2 then the voter has a quadratic loss function and their disutility is the square of the minkowski distance. This has the effect of causing utility to fall slowly at first as they evaluate alternatives closer to their ideal, but then once an alternative is sufficently far away utility falls much faster than in the linear case.
`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.

This function will find the salience weighted Minkowski Utility 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, a set of 'sailence' weights for each policy dimension and a loss order. Each voter can have a different loss order for their loss function.

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

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

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

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