Package 'sate'

Calculates probability a jury will find defendant guilty based on juror preferences

Description

Calculates the probability that a jury of size jury_n finds defendant guilty given preferences of the jury pool (input as sample_pg). Does not estimate uncertainty (use as.jury.stats function for inferential statistics).

Usage

as.jury.point(
  sample_pg,
  jury_n = 12,
  pstrikes = 0,
  dstrikes = 0,
  accuracy = 0.15,
  simulate = FALSE
)

Arguments

sample_pg	Proportion of jurors who favor a guilty verdict. Can be a single number between 0 and 1, or a vector of such numbers.
jury_n	Size of the jury (i.e. 6, 8, or 12); default value is 12.
pstrikes	Number of peremptory strikes by prosecution; default value is 0.
dstrikes	Number of peremptory strikes by defendant; default value is 0.
accuracy	Accuracy of parties' peremptory strikes; a number between 0 and 1; default value is .15.
simulate	Simulation control. Use 'FALSE' (default) for deterministic Markov model values, 'TRUE' for simulation with defaults ('nDraws=10000', 'seed=NULL'), or a named list like 'list(nDraws=5000, seed=12345)'.

Value

Returns the probability jury finds defendant guilty (if sample_pg is a single number) or vector of such probabilities (if sample_pg is a vector).

Examples

library(sate)
   as.jury.point(sample_pg = .50)

   as.jury.point(sample_pg = 10/12)

   as.jury.point(sample_pg = .50, simulate = TRUE)

---

Calculates probability a jury will find defendant guilty based on juror preferences, with standard error and confidence interval

Description

Calculates probability jury finds defendant guilty based on verdicts preferences of jury pool. Also reports standard error and confidence interval of estimate (use as.jury.point function for estimate only).

Usage

as.jury.stats(
  sample_pg,
  sample_n,
  jury_n = 12,
  pstrikes = 0,
  dstrikes = 0,
  accuracy = 0.15,
  digits = 3,
  simulate = FALSE
)

Arguments

sample_pg	Proportion of jurors who favor a guilty verdict; a number between 0 and 1.
sample_n	Size of sample used to estimate sample_pg.
jury_n	Size of the jury (i.e. 6, 8, or 12); default value is 12.
pstrikes	Number of peremptory strikes by prosecution; default value is 0.
dstrikes	Number of peremptory strikes by defendant; default value is 0.
accuracy	Accuracy of parties' peremptory strikes; a number between 0 and 1; default value is .15.
digits	Number of digits to report after decimal places; default value is 3.
simulate	Simulation control for uncertainty estimation. Use 'FALSE' (default) for analytic method, 'TRUE' for simulation with defaults ('nDraws=10000', 'seed=NULL'), or a named list like 'list(nDraws=5000, seed=12345)'.

Value

Returns a one-row data.frame with columns: P(G), SE, MOE, Lower 5

Examples

library(sate)
   as.jury.stats(sample_pg=.50, sample_n=830)

   as.jury.stats(sample_pg=10/12, sample_n=295)

   as.jury.stats(sample_pg=.50, sample_n=830, simulate=TRUE)

   as.jury.stats(sample_pg=.50, sample_n=830,
                 simulate=list(nDraws=5000, seed=12345))

---

Creates the shell of a plot showing relationship between jury pool preferences and jury verdict probabilities

Description

Creates the shell of a plot showing relationship between jury pool preferences and jury verdict probabilities, optional argument to modify main, xlab, and ylab labels, includes grid lines.

Usage

basic.plot.grid(main, xlab, ylab)

Arguments

main	Main title for plot (optional), default is no main title.
xlab	X-axis label for plot (optional), default is "Jurors' Verdict Preferences, P(g)".
ylab	Y-axis label for plot (optional), default is "Jury Verdict Probabilities, P(G)".

Value

No return value; function creates a plot.

Examples

library(sate)
   basic.plot.grid()

   basic.plot.grid(main="Death Sentencing Analysis", xlab="Jurors' Sentencing Preferences, P(d)",
                   ylab="Jury Verdict Probabilities, P(D)")

---

Creates the shell of a plot used to display estimate of harm relative to harm threshold

Description

Creates the shell of a plot used for compact display estimate of harm estimate relative to harm thresholds.

Usage

compact_harm_plot()

Value

No return

Examples

library(sate)
   compact_harm_plot()

---

Estimates juror-level differences based on sample statistics (from survey)

Description

Calculates juror-level statistics and differences based on sample statistics (from a survey) supplied by user.

Usage

compare.juror.stats(pg_actual, n_actual, pg_hypo, n_hypo, digits = 3)

Arguments

pg_actual	The proportion of jurors who favor a guilty verdict in the actual trial condition (the trial with error).
n_actual	The size of the sample used to estimate pg_actual.
pg_hypo	The proportion of jurors who favor a guilty verdict in the hypothetical trial condition (the fair trial without error).
n_hypo	The size of the sample used to estimate pg_hypo.
digits	Number of digits to report after decimal places; default value is 3.

Value

Returns a list of juror-level statistics to assess the effect of a trial error or omission on juror preferences. Returned list includes statistics for the actual trial, the hypothetical trial, and the difference between them.

Examples

library(sate)
   compare.juror.stats(pg_actual=.70, n_actual=400, pg_hypo=.60, n_hypo=450)

   compare.juror.stats(pg_actual=.75, n_actual=450, pg_hypo=.65, n_hypo=350)

---

Estimates jury-level differences based on juror-level statistics with inferential statistics

Description

Calculates jury-level statistics and differences based on juror-level statistics supplied by user.

Usage

compare.jury.stats(
  pg_actual,
  n_actual,
  pg_hypo,
  n_hypo,
  jury_n = 12,
  pstrikes = 0,
  dstrikes = 0,
  accuracy = 0.15,
  digits = 3,
  simulate = FALSE
)

Arguments

pg_actual	The proportion of jurors who favor a guilty verdict in the actual trial condition (the trial with error).
n_actual	The size of the sample used to estimate pg_actual.
pg_hypo	The proportion of jurors who favor a guilty verdict in the hypothetical trial condition (the fair trial without error).
n_hypo	The size of the sample used to estimate pg_hypo.
jury_n	Size of the jury (i.e. 6, 8, or 12); default value is 12.
pstrikes	Number of peremptory strikes by prosecution; default value is 0.
dstrikes	Number of peremptory strikes by defendant; default value is 0.
accuracy	Accuracy of parties' peremptory strikes; a number between 0 and 1; default value is .15.
digits	Number of digits to report after decimal places; default value is 3.
simulate	Simulation control for uncertainty estimation. Use 'FALSE' (default) for analytic method, 'TRUE' for simulation with defaults ('nDraws=10000', 'seed=NULL'), or a named list like 'list(nDraws=5000, seed=12345)'.

Value

Returns a list of jury-level statistics to assess effect of a trial error. Returned list includes statistics for actual jury, hypothetical jury, and the difference between them.

Examples

library(sate)
   compare.jury.stats(pg_actual=.70, n_actual=400, pg_hypo=.60, n_hypo=450)

   compare.jury.stats(pg_actual=.75, n_actual=450, pg_hypo=.65, n_hypo=350,
                      jury_n=6, pstrikes=3, dstrikes=3)

   compare.jury.stats(pg_actual=.70, n_actual=400, pg_hypo=.60, n_hypo=450,
                      simulate=TRUE)

---

Deliberation function

Description

The deliberate function returns a jury verdict based on a simulation of deliberation as a modified tug-of-war between two verdict factions. Can be called directly, but is meant to be called many times to generate verdict probabilities based on g_votes and jury_n values. Requires '0 <= g_votes <= jury_n'.

Usage

deliberate(g_votes, jury_n)

Arguments

g_votes	Initial number of votes for guilty verdict (same as K value).
jury_n	Size of the jury (i.e. 4, 6, 8, 12, or 16).

Value

Returns "G" (guilty verdict), "NG" (not guilty verdict), or 'NA' if either input is 'NA'.

Examples

library(sate)
   deliberate(g_votes=10, jury_n=12)

   deliberate(g_votes=4, jury_n=6)

---

Deliberation function for civil trials (proposed)

Description

The deliberate function returns a jury verdict based on a simulation of deliberation as a tug-of-war between two verdict factions. The civil version of deliberate does not have presumption in favor of either party. Can be called directly, but is meant to be called many times to generate verdict probabilities based on p_votes and jury_n values. Requires '0 <= p_votes <= jury_n'.

Usage

deliberate.civil(p_votes, jury_n)

Arguments

p_votes	Initial number of votes for plaintiff.
jury_n	Size of the jury (i.e. 4, 6, 8, 12, or 16).

Value

Returns "P" (plaintiff verdict), "D" (defendant verdict), or 'NA' if either input is 'NA'.

Examples

library(sate)
   deliberate.civil(p_votes=8, jury_n=12)

   deliberate.civil(p_votes=5, jury_n=6)

---

Encodes Cloud Research respondent information in form suitable for calculating sampling weights

Description

Encodes Cloud research respondent information with names and values suitable for calculating sampling weights. All variables encoded and added to dataset are booleans. The variable respondent_na is TRUE if the respondent's information is "Prefer not to say" or missing on any variable.

Usage

encode.cloud.respondent.variables(dataset)

Arguments

dataset

Data frame containing Cloud Research respondent demographic information. Required columns are: Race, Education, Household.Income, Age, Gender, and Ethnicity. Age must be numeric.

Value

Returns dataset with encoded variables added: black, ba_or_more, hhincome_over50k, age35plus, woman, hispanic, and respondent_na.

Examples

library(sate)

   example <- data.frame(Race = sample(x=c("Black or African American", "Other"),
                                       size=10, replace=TRUE),
                         Education = sample(x=c("Bachelor's degree (for example: BA, AB, BS)",
                                            "Other"), size=10, replace=TRUE),
                         Household.Income = sample(x=c("$70,000-$79,999", "Other"),
                                                   size=10, replace=TRUE),
                         Age = sample(x=18:80, size=10, replace=TRUE),
                         Gender = sample(x=c("Woman", "Man", "Prefer not to say"),
                                         size=10, replace=TRUE),
                         Ethnicity = sample(x=c("No, not of Hispanic, Latino, or Spanish origin",
                                            "Other"), size=10, replace=TRUE))
   dataset.encoded <- encode.cloud.respondent.variables(dataset=example)

---

Calculates vector of probabilities that jury with jury_n will return a guilty verdict

Description

Calculates a vector of probabilities that a jury with jury_n will return a guilty verdict. The vector represents P(G|k) for 0, 1, 2, ... , jury_n where k is the number of jurors initially in favor of guilty verdict.

Usage

get_pG_by_k(jury_n = 6)

Arguments

jury_n

Size of the jury (i.e. 6, 8, or 12); default value is 6.

Value

Returns a vector of probabilities for guilty verdict of size jury_n + 1.

Examples

library(sate)
   get_pG_by_k(10)

   get_pG_by_k(jury_n=12)

---

Plots jury-level differences based on juror-level statistics with effect-on-defendant displayed

Description

Plots jury-level differences based on juror-level statistics supplied by user. Point estimates supplemented by confidence intervals. Effect-on-defendant also plotted.

Usage

graph.effect.defendant(
  pg_actual,
  n_actual,
  pg_hypo,
  n_hypo,
  jury_n = 12,
  pstrikes = 0,
  dstrikes = 0,
  accuracy = 0.15,
  simulate = FALSE
)

Arguments

pg_actual	The proportion of jurors who favor a guilty verdict in the actual trial condition (the trial with error).
n_actual	The size of the sample used to estimate pg_actual.
pg_hypo	The proportion of jurors who favor a guilty verdict in the hypothetical trial condition (the fair trial without error).
n_hypo	The size of the sample used to estimate pg_hypo.
jury_n	Size of the jury (i.e. 6, 8, or 12); default value is 12.
pstrikes	Number of peremptory strikes by prosecution; default value is 0.
dstrikes	Number of peremptory strikes by defendant; default value is 0.
accuracy	Accuracy of parties' peremptory strikes; a number between 0 and 1; default value is .15.
simulate	Simulation control passed to 'compare.jury.stats' and 'as.jury.stats'. Use 'FALSE' (default), 'TRUE', or a named list like 'list(nDraws=5000, seed=12345)'. For graphing speed, 'TRUE' uses 'nDraws=2000' by default.

Value

No return (creates plots)

Examples

library(sate)
   graph.effect.defendant(pg_actual=.70, n_actual=400, pg_hypo=.60, n_hypo=450)

   graph.effect.defendant(pg_actual=.75, n_actual=450, pg_hypo=.65, n_hypo=350,
                         jury_n=6, pstrikes=3, dstrikes=3)

   graph.effect.defendant(pg_actual=.70, n_actual=400, pg_hypo=.60, n_hypo=450, simulate=TRUE)

---

Plots probability of a guilty verdict with confidence interval based on juror-level statistics

Description

Plots probability of guilty verdict with confidence interval based on juror-level statistics supplied by user. Similar to graph.effect.defendant, but plots one condition.

Usage

graph.estimate(
  sample_pg,
  sample_n,
  jury_n = 12,
  pstrikes = 0,
  dstrikes = 0,
  accuracy = 0.15,
  simulate = FALSE
)

Arguments

sample_pg	The proportion of jurors who favor a guilty verdict in the sample condition
sample_n	The size of the sample used to estimate sample_pg_actual
jury_n	Size of the jury (i.e. 6, 8, or 12); default value is 12.
pstrikes	Number of peremptory strikes by prosecution; default value is 0.
dstrikes	Number of peremptory strikes by defendant; default value is 0.
accuracy	Accuracy of parties' peremptory strikes; a number between 0 and 1; default value is .15.
simulate	Simulation control passed to 'as.jury.stats'. Use 'FALSE' (default), 'TRUE', or a named list like 'list(nDraws=5000, seed=12345)'. For graphing speed, 'TRUE' uses 'nDraws=2000' by default.

Value

No return (creates plot)

Examples

library(sate)
   graph.estimate(sample_pg=.70, sample_n=400)

   graph.estimate(sample_pg=.75, sample_n=450, jury_n=6, pstrikes=3, dstrikes=3)

   graph.estimate(sample_pg=.70, sample_n=400, simulate=TRUE)

---

Dataset of Observed Deliberations

Description

A compilation of observed jury deliberations from multiple studies used to analyze relationship between initial state of jury and probability of verdict.

Usage

observed.deliberations

Format

A data frame with 2382 rows and 7 variables.

idnum

Internal identification number.

prop_jurors_g

Proportion of jurors initially in favor of guilty/death verdict.

jury_size

Size of jury.

guilty_verdict

Did jury render guilty/death verdict? 1 = yes, 0 = no.

six_person_jury

Deliberation by six-person jury? 1 = yes, 0 = no.

death_penalty

Was jury deliberating death penalty? 1 = yes, 0 = no.

source

Source of data. Devine_2001 = Devine et al. (2001) table 6 without Sandys & Dillehey (1995); Devine_2004 = Devine et al. (2004) table 2; Devine_2007 = Devine et al. (2007) with correction for undecideds suggested by Kerr and McCoun (2012); Sandys_1995 = Sandys & Dillehey (1995) with correction for undecideds suggested by Kerr and McCoun (2012); CJP_2015 = Capital Jury Project from Devine & Kelly (2015), some imputed prop_jurors_g values; NCSC_LA = Hannaford-Agor et al. (2001), NCSC Study, Los Angeles site trials, with identifying number; NCSC_AZ = Hannaford-Agor et al. (2001), NCSC Study, Maricopa site trials, with identifying number; NCSC_NY = Hannaford-Agor et al. (2001), NCSC Study, Bronx site trials, with identifying number; NCSC_DC = Hannaford-Agor et al. (2001), NCSC Study, Washington, DC site trials, with identifying number;

Source

Compilation of multiple sources, see source variable.

---

verdict probabilities based on jury pool sentiment for ordered verdict options.

Description

verdict probabilities based on jury pool sentiment for ordered verdict options.

Usage

prob_ord_from_pool(jury_n, verdict_options, verdict_props, digits = NULL)

Arguments

jury_n	Integer. Number of jurors.
verdict_options	Character vector of ordered verdict labels (e.g., 'c("NG","M2","M1")'). Order matters: left = most lenient. Labels must be non-missing, non-empty, and unique.
verdict_props	Numeric vector specifying proportion of jurors who support the respective verdict_options in the population from which jurors are drawn. (e.g., 'c(.25,.50,.25)'). Must correspond to verdict_options, contain non-missing finite values, be non-negative, and sum to a positive value.
digits	Integer. Optional, number of digits to round in the returned matrix.

Value

A vector of length K that are probabilities of the ordered verdicts.

See Also

[transition.matrix.ordered]

Examples

library(sate)

# Three-verdict ordered model with a 12-person jury:
prob_ord_from_pool(12, c("NG", "M2", "M1"), c(.25,.50,.25), digits=3)

---

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)

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.

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.

See Also

[transition.matrix.ordered]

Examples

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)

---

Generates the distribution of initial votes for guilty verdict on juries

Description

Calculates and returns probability distribution of initial votes for guilty verdict from 0:jury_n with options for peremptory strikes and strike accuracy. To select jury without strikes, keep pstrikes=0 and dstrikes=0.

Usage

select.with.strikes(
  p_g,
  jury_n = 12,
  pstrikes = 0,
  dstrikes = 0,
  accuracy = 0.15
)

Arguments

p_g	The proportion of jurors in the jury pool who favor a guilty verdict
jury_n	Size of the jury (i.e. 6, 8, or 12); default value is 12.
pstrikes	Number of peremptory strikes by prosecution; default value is 0.
dstrikes	Number of peremptory strikes by defendant; default value is 0.
accuracy	Accuracy of parties' peremptory strikes; a number between 0 and 1; default value is .15.

Value

A vector of probabilities for 0:jury_n initial guilty votes

Examples

library(sate)
   select.with.strikes(p_g=.70, jury_n=6)

   select.with.strikes(p_g=.75, jury_n=12, pstrikes=6, dstrikes=10)

---

Estimates jury-level probability of guilty verdict based on juror-level statistics based on empirical data

Description

Returns estimate of the probability of guilty verdict based on juror-level statistics supplied by user. Also reports inferential statistics. Results are based on an empirical model with greater uncertainty than as.jury.stats function.

Usage

sim.as.jury.stats(
  sample_pg,
  sample_n,
  jury_n = 12,
  pstrikes = 0,
  dstrikes = 0,
  accuracy = 0.15,
  digits = 3,
  nDraws = 10000,
  seed = NULL
)

Arguments

sample_pg	The proportion of jurors who favor a guilty verdict in the jury pool
sample_n	The size of the sample used to estimate sample_pg
jury_n	Size of the jury (i.e. 6, 8, or 12); default value is 12.
pstrikes	Number of peremptory strikes by prosecution; default value is 0.
dstrikes	Number of peremptory strikes by defendant; default value is 0.
accuracy	Accuracy of parties' peremptory strikes; a number between 0 and 1; default value is .15.
digits	Number of digits to report after decimal places; default value is 3.
nDraws	The number of simulations used to generate results. Should be very large number (default = 10000).
seed	Optional non-negative integer seed for replication. Default is NULL (no seeding).

Value

Returns a one-row data.frame with columns: P(G), SE, MOE, Lower 5

Examples

library(sate)
   sim.as.jury.stats(sample_pg=.50, sample_n=830, nDraws=500)

   sim.as.jury.stats(sample_pg=10/12, sample_n=295, pstrikes=6, dstrikes=10, nDraws=1000)

---

Estimates jury-level differences based on juror-level statistics using simulations based on empirical data

Description

Calculates jury-level differences based on juror-level statistics supplied by user. Results based on empirical data, inferential statistics produced via simulations.

Usage

sim.compare.jury.stats(
  pg_actual,
  n_actual,
  pg_hypo,
  n_hypo,
  jury_n = 12,
  digits = 3,
  pstrikes = 0,
  dstrikes = 0,
  accuracy = 0.15,
  seed = NULL,
  nDraws = 10000
)

Arguments

pg_actual	The proportion of jurors who favor a guilty verdict in the actual trial condition (the trial with error).
n_actual	The size of the sample used to estimate pg_actual.
pg_hypo	The proportion of jurors who favor a guilty verdict in the hypothetical trial condition (the fair trial without error).
n_hypo	The size of the sample used to estimate pg_hypo.
jury_n	Size of the jury (i.e. 6, 8, or 12); default value is 12.
digits	Number of digits to report after decimal places; default value is 3.
pstrikes	Number of peremptory strikes by prosecution; default value is 0.
dstrikes	Number of peremptory strikes by defendant; default value is 0.
accuracy	Accuracy of parties' peremptory strikes; a number between 0 and 1; default value is .15.
seed	Optional non-negative integer seed for replication. Default is NULL (no seeding).
nDraws	The number of simulations used to generate results. Should be very large number (default = 10000).

Value

Returns a list of jury-level statistics to assess effect of a trial error.

Examples

library(sate)
   sim.compare.jury.stats(pg_actual=.70, n_actual=400, pg_hypo=.60, n_hypo=450, nDraws=500)

   sim.compare.jury.stats(pg_actual=.75, n_actual=450, pg_hypo=.65, n_hypo=350,
                      seed=12345, nDraws=1000)

---

State Demographic Information

Description

A dataset with demographic statistics at state level plus national-level that may be used for calculating sample weights. Includes information related to race, educational attainment, household income, age, gender, and ethnicity.

Usage

state.demographic.info

Format

A data frame with 52 rows and 8 variables.

state

Name of state

StateID

Two-letter abbreviation for state. USA for nation.

black

Proportion of state population who identify as black (African American), per US Census Bureau.

ba_or_more

Proportion of adult (18+) population who have attained a BA degree or more, per US Census Bureau.

hhincome_over50k

Proportion of state population with household income of $50,000 or more, per US Census Bureau.

age35plus

Proportion of adult (18+) population age 35 or older, per US Census Bureau.

woman

Proportion of state population who identify as women, per US Census Bureau.

hispanic

Proportion of state population who identify as Hispanic, per US Census Bureau.

Source

U.S. Census Bureau, American Community Survey, 5-Year Estimates.

---

Looks up and returns key demographic statistics for target state to be used for calculating sample weights

Description

Looks up and returns six key demographic statistics for a target state to be used for calculating sample weights. State-level population statistics from U.S. Census Bureau, American Community Survey 5-year estimates. Data from state.demographic.info, a saved datafile in sate package.

Usage

target.population.demographics(state)

Arguments

state

The target state, input as two-letter abbreviation (i.e., "GA" "TX" or "FL"). If no state specified, will use "USA".

Value

A one row data.frame with the following statistics: black, ba_or_more, hhincome_over50k, age35plus, woman, hispanic

Examples

library(sate)
   target.population.demographics(state="FL")

   target.population.demographics()   # will return stats for USA

---

Creates and Returns a Transition Probability Matrix for Deliberating Criminal Jury.

Description

Returns a (jury_n + 1) by (jury_n + 1) matrix of probabilities. Columns represent current state and rows represent next state. Column values sum to 1. Depending on use, you may want to transpose rows and columns.

Usage

transition.matrix(jury_n)

Arguments

jury_n

The number of jurors.

Value

A matrix of transition probabilities.

Examples

library(sate)

   transition.matrix(6)

   transition.matrix(jury_n=12)

---

Build column-stochastic transition matrix for ordered verdict options

Description

Constructs the full **column-stochastic** Markov transition matrix \(P\) for a jury deliberation model with an **ordered** set of verdict options (least to most punitive). Transient states are all compositions of 'jury_n' jurors across the 'verdict_options'; absorbing states are the 'K' unanimity vertices (one per verdict), appended at the end in the same order as 'verdict_options'.

The transition from a transient state is built by applying your **2-option step rule** independently at each adjacent *cut* between options and combining those suggestions with **equal weight across cuts**. For cut 'r' (between options 'r' and 'r+1'), let 'g = sum(counts[(r+1):K])' be the number on the **more punitive** side; compute

$p_\text{up} = \left(0.5\frac{g-1}{n} + 0.25\right)^2,\quad p_\text{down} = \left(1 - 0.5\frac{g-1}{n} - 0.25\right)^2,\quad p_\text{stay} = 1 - p_\text{up} - p_\text{down}.$

Map "up" to moving one juror across the cut toward the more punitive option, "down" toward the less punitive option; pool all "stay" mass (and any illegal move mass at boundaries) into the **self-loop** so each column still sums to 1.

Usage

transition.matrix.ordered(jury_n, verdict_options, digits = NULL)

Arguments

jury_n	Integer. Size of the jury (number of jurors), 'jury_n >= 1'.
verdict_options	Character vector of **ordered** verdict labels from least to most punitive, e.g. 'c("NG","M2","M1")' or 'c("NG","M3","M2","M1")'. Labels must be non-missing, non-empty, and unique. The order defines which options are adjacent.
digits	Optional integer. If supplied, round the returned matrix to this many decimals and then re-normalize each column to remain column-stochastic. Defaults to 'NULL' (no rounding).

Details

* Absorbing columns (the last 'K') are identity columns (unanimity stays put). * Self-loops collect "stay" mass from all cuts and any mass from moves that are illegal at boundaries (e.g., trying to move from an empty option). * Providing 'digits' is meant for tidy printing; for numerical work you may prefer to leave 'digits = NULL' to keep full precision.

Value

A column-stochastic matrix 'P' of size $S \times S$, where $S = \binom{n+K-1}{K-1}$ is the number of compositions of 'jury_n' into 'K' parts (all states), ordered with **transients first** and then the 'K' unanimity absorbing states in the order of 'verdict_options'. The matrix carries metadata on 'attr(P, "meta")' as a list with elements:

• 'states' - list of length-'K' integer count vectors for each state, in column order;

• 'idx' - environment mapping comma-joined count vectors to column/row indices;

• 'T', 'S', 'K', 'n' - counts (transients, total states, #options, #jurors);

• 'verdict_options' - the label vector you supplied.

See Also

prob.ordered.verdicts for solved absorption probabilities (including appended unanimity starts) built on top of this transition matrix.

Examples

# 3 jurors, 3 options (NG < M2 < M1), equal cut weights
P <- transition.matrix.ordered(3, c("NG","M2","M1"))
dim(P); colSums(P)                        # columns sum to 1
attr(P, "meta")$verdict_options           # labels carried in metadata

# Tidy print:
transition.matrix.ordered(3, c("NG","M2","M1"), digits = 3)

# 4 options (NG < M3 < M2 < M1)
P4 <- transition.matrix.ordered(3, c("NG","M3","M2","M1"))

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Calculates survey weights given respondent information and target population demographics

Description

Calculates survey weights given respondent information and target population demographics. Respondent demographic info must be properly encoded in respondentdata to work with targetdata. If respondent demographic info is missing, the respondent's weight will be coded 1. Weight values trimmed so that no weights are greater than 6 or less than .1.

Usage

weights_for_population(respondentdata, targetdata)

Arguments

respondentdata	Data frame with encoded respondent demographic information (use encode.cloud.respondent.variables to prepare). Must include: ParticipantId, black, ba_or_more, hhincome_over50k, age35plus, woman, hispanic, respondent_na.
targetdata	A one-row data.frame (or named vector) with the following statistics in [0, 1]: black, ba_or_more, hhincome_over50k, age35plus, woman, hispanic (use target.population.demographics to obtain).

Value

Returns respondentdata with raked sampling weights encoded.

Examples

library(sate)

   example_n <- 100
   example <- data.frame(Race = sample(x=c("Black or African American", "Other"),
                                       size=example_n, replace=TRUE),
                         Education = sample(x=c("Bachelor's degree (for example: BA, AB, BS)",
                                            "Other"), size=example_n, replace=TRUE),
                         Household.Income = sample(x=c("$70,000-$79,999", "Other"),
                                                   size=example_n, replace=TRUE),
                         Age = sample(x=18:80, size=example_n, replace=TRUE),
                         Gender = sample(x=c("Woman", "Man", "Prefer not to say"),
                                         size=example_n, replace=TRUE),
                         Ethnicity = sample(x=c("No, not of Hispanic, Latino, or Spanish origin",
                                            "Other"), size=example_n, replace=TRUE),
                         ParticipantId = 1:example_n)
   respondents.encoded <- encode.cloud.respondent.variables(dataset=example)

   pop.targets <- target.population.demographics(state="FL")

   respondents.weighted <- weights_for_population(respondentdata = respondents.encoded,
                                                  targetdata = pop.targets)

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