prob.ordered.verdicts: Absorption probabilities for ordered-category jury models

Description

Compute the probability that an ordered-category Markov chain on jury vote counts will eventually absorb at each unanimous verdict, starting from any transient (non-unanimous) composition. Internally, this constructs the transition matrix with `transition.matrix.ordered()` **using its defaults**, i.e., equal cut lines (no lambda weighting).

Usage

prob.ordered.verdicts(jury_n, verdict_options, digits = NULL, collab = TRUE)

Value

A numeric K by T+K matrix of absorption probabilities. Rows index absorbing verdicts in `verdict_options`. Columns index starting states: first all transient compositions, then each unanimity composition (one per verdict). If `collab = TRUE`, row/column names are added.

Arguments

jury_n: Integer. Number of jurors.
verdict_options: Character vector of ordered verdict labels (e.g., `c("NG","Lesser","G")`). Order matters: left = most lenient.
digits: Integer. Number of digits to round in the returned matrix. Default `3`.
collab: Logical. If `TRUE` (default), attach human-friendly row/column labels: rows are verdict names; columns are starting states (transients first, then unanimities).

Details

Let \(P\) be the transition matrix returned by `transition.matrix.ordered(jury_n, verdict_options)`, with meta attributes providing: - `T`: number of transient states, - `K`: number of absorbing states (equal to `length(verdict_options)`), - `states`: list of length `T + K` of count vectors (per state), - `n`: the jury size, - `verdict_options`: the verdict labels.

Examples

Run this code

library(sate)

# Three-verdict ordered model with a 12-person jury:
prob.ordered.verdicts(12, c("NG", "M2", "M1"))

# Probability of ultimately unanimous "Lesser" starting from A=6, B=4, C=2:
prob.ordered.verdicts(12, c("A","B","C"), digits = 3)