election_list_functions: Create election list for analysis

In aeggers/pivotprobs: Methods for estimating the probability of ties and other important election events.

Create election list for analysis

Description

An election list represents an election in a minimal way: it contains the electorate size, the ballot format, and a list of "election events", i.e. situations in which a single ballot can affect the outcome in a given way. It also contains a label for the voting system, e.g. "positional". An election list is passed to the election_event_probs() function to compute the probability of each election event given a model of voting outcomes.

Usage

plurality_election(n = 1000, k = 4, max_pivot_event_degree = 1)

pr_election(n = 1000, M = 3)

positional_election(n = 1000, s = 0.5)

irv_election(n = 1000, s = 0)

kemeny_young_election(n = 1000)

Arguments

n	The size of the electorate. This (slightly) affects the conditions for election events in the election list (e.g. the region in which one candidate is more than one vote ahead of another). n is also used when computing pivot event probabilities from an election list in election_event_probs(), where higher n means lower probability.
k	The number of candidates in plurality.
max_pivot_event_degree	If 1, we consider two-way (near) ties in plurality. If 2, we also consider three-way (near) ties.
s	The value of a second-ranking in a three-candidate positional election, where a top ranking is worth 1 and a bottom ranking is worth 0.

Details

An election list contains the electorate size n, an ordinal flag indicating whether this is an ordinal or single-ballot voting system, and a list of election events. For each event, the election list indicates

• conditions under which the event takes place, and

• which candidate wins given that this event takes place as a function of which additional ballot is submitted.

These functions produce plain lists, so functions can be written for further election methods.

The election methods provided are:

• plurality_election(), where each voter votes for one of k>=3 candidates and the candidate with the most votes wins.

• positional_election(), where each voter ranks the three candidates and the candidate with the highest score wins, with each top ranking worth 1 point, each bottom ranking worth 0 points, and each middle ranking worth s points. For now we can only handle 3 candidates. (I have written code to handle more, but the QHull functions seem to have trouble with the geometry.)

• irv_election() (instant-runoff), where each voter ranks the three candidates and the winner is determined by a process of elimination. The ballots are initially tallied using a positional method; the most commonly used option is plurality, i.e. s=0.) The lowest-scoring candidate is eliminated. Given three candidates, the winner is then determined according to which of the remaining candidates is ranked higher on more ballots.

• kemeny_young_election() (maximin), where any candidate who defeats all others in a pairwise comparison (i.e. is ranked higher on more ballots) is the winner and, if there is no such candidate, the winner is the candidate who is defeated by the smallest margin.

Examples

plurality_election(k = 3)
positional_election(s = .5) # borda count
irv_election()
kemeny_young_election()

aeggers/pivotprobs documentation built on Oct. 28, 2024, 9:46 a.m.