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

Description

Calculates the probability that jury of size jury_n finds defendant guilty given on preferences of jury pool (inputted 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
)

Arguments

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)

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
)

Arguments

Value

Returns the probability jury finds defendant guilty.

Examples

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

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

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

Value

No return

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

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
)

Arguments

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)

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.

Usage

deliberate(g_votes, jury_n)

Arguments

Value

Returns "G" (guilty verdict) or "NG" (not guilty verdict).

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.

Usage

deliberate.civil(p_votes, jury_n)

Arguments

Value

Returns "P" (plaintiff verdict) or "D" (defendant verdict).

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

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 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

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
)

Arguments

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)

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
)

Arguments

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)

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.

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

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)

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

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)

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

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 = 12345
)

Arguments

Value

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

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 = 12345,
  nDraws = 10000
)

Arguments

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

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

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 → 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

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"))

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 the target.demographics. 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

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)