CAST.calc.sample {elec}

Construct a sample for auditing using CAST

Description

Collection of functions for planning and evaluating results of a CAST election audit. CAST is a system devised by Dr. Philip B., Stark, UC Berkeley Department of Statistics.

CAST.calc.sample determines what size SRS sample should be drawn to have a reasonable chance of certification if the election does not have substantial error. It returns an audit.plan. CAST.sample takes the audit.plan and draws a sample to audit. CAST.audit takes audit data (presumably from the audit of the sample drawn in previous step) and analyzes it.

Make an audit.plan given reported results for an election. It gives back what to do for a single stage. If stages is > 1, then it adjusts beta appropriately.

Usage

CAST.calc.sample(
  Z,
  beta = 0.9,
  stages = 1,
  t = 3,
  as.taint = FALSE,
  small.cut = NULL,
  strata = NULL,
  drop = NULL,
  method = c("select", "binomial", "hypergeometric"),
  calc.e.max = TRUE,
  bound.function = maximumMarginBound
)

Arguments

Z

elec.data object (voter matrix)

beta

the confidence level desired - overall chance of correctly escalating a bad election to full recount

stages

number of auditing stages. Each stage will have the same confidence level, determined by a function of beta. A value of 1 is a single-stage audit.

t

The maximum amount of error, in votes, expected. Threshold error for escalation – if >= 1 then number of votes, otherwise fraction of margin.

as.taint

Boolean value. TRUE means interpret $t$ as a taint in $[0,1]$ by batch (so the threshold error will be batch-specific). FALSE means interpret $t$ as a proportion of the margin or as number of votes (as described above).

small.cut

Cut-off in votes–any precincts with potential error smaller than this value will not be audited and be assumed to be worst case error.

strata

Name of the stratification column of Z. Not needed if audit plan also being passed in case of CAST.sample. NULL means single strata.

drop

Vector of precincts to drop for whatever reasons (such as they are already known). This is a vector of TRUE/FALSE.

method

Method of calculation.

calc.e.max

Should the e.max be taken as given, or recalculated?

bound.function

What function should be used to calculate worst-case potential error of precincts.

Author(s)

Luke W. Miratrix

References

Philip B. Stark. CAST: Canvass Audits by Sampling and Testing. University of California at Berkeley Department of Statistics, 2009. URL: http://statistics.berkeley.edu/~stark/Preprints/cast09.pdf. Also see http://www.stat.berkeley.edu/~stark/Vote/index.htm for other relevant information.

See Also

elec.data for a description of the object that holds precinct-level vote records. See tri.calc.sample for a PPEB auditing method. See CAST.calc.opt.cut for calculating optimal cut-offs to keep needed sample size low. Also see sim.race, do.audit, make.sample, and make.truth for doing simulation studies of this method.

Examples

        ## Make an example cartoon race (from Stark paper)
	Z = make.cartoon()

        ## What should we do?
	samp.info = CAST.calc.sample( Z )
	samp.info

        ## Draw a sample.
	samp = CAST.sample( Z, samp.info$ns )
        samp

        ## Analyze what a CAST audit of santa cruz would entail
        data(santa.cruz)
        Z = elec.data( santa.cruz, C.names=c("leopold","danner") )
        CAST.calc.sample( Z, beta=0.75, stages=1, t=5, small.cut=60)