trinomial.bound {elec}

Auditing with the Trinomial Bound: trinomial.bound and trinomial.audit

Description

This method makes a contour plot of the optimization problem.

Usage

trinomial.bound(
  n = 11,
  k = 2,
  d = 40,
  e.max = 100,
  xlim = c(0.4, 1),
  ylim = c(0, 0.55),
  alpha.lvls = c(10),
  zero.threshold = 0.3,
  tick.lines = NULL,
  alpha.lwd = 2,
  bold.first = FALSE,
  plot = TRUE,
  p.value.bound = NULL,
  grid.resolution = 300,
  ...
)

Arguments

n

Size of the sample (not precincts, but samples which could potentially be multiple samples of the same precinct).

k

The number of positive taints found in sample.

d

The maximum size of a small taint. This is the threshold for being in the middle bin of the trinomial. All taints larger than d would be in the largest error bin.

e.max

The size of the largest error bin. Typically 100 (for percent) or 1.

xlim

Range of possible values of p0 worth considering

ylim

Range of possible values of pd worth considering

alpha.lvls

List of alphas for which bounds should be calculated. The first is the one that will be returned. The others will be graphed.

zero.threshold

Since the method calculates on a numerical grid, what difference between alpha and the calculated probabilty should be considered no difference.

tick.lines

A list of bounds. For these bound levels, add tick-lines (more faint lines) to graph

alpha.lwd

Line width for alpha line.

bold.first

TRUE/FALSE. Should first alpha line be in bold.

plot

Should a plot be generated.

p.value.bound

What is the bound (1/U) that would correspond to the entire margin. Finding the alpha corresponding to this bound is a method for finding the p-value for the trinomial bound test.

grid.resolution

How many divisions of the grid should there be? More gives greater accuracy in the resulting p-values and bounds.

...

Extra arguments passed to the plot command.

Details

Note: alphas are multiplied by 100 to get in percents.

Value

List with characteristics of the audit and the final results.

n

Size of sample.

k

Number of non-zero taints.

d

Threshold for what a small taint is.

e.max

The worst-case taint.

max

The upper confidence bound for the passed alpha-level.

p

A length three vector. The distribution (p0, pd, p1) that achieves the worst case.

p.value

The p.value for the test, if a specific worst-case bound 1/U was passed via p.value.bound.

References

See Luke W. Miratrix and Philip B. Stark. (2009) Election Audits using a Trinomial Bound. https://www.stat.berkeley.edu/~stark/Vote/index.htm

See Also

See elec.data for information on the object that holds vote counts. See tri.sample for drawing the actual sample. See tri.calc.sample for figuring out how many samples to draw. See tri.audit.sim for simulating audits using this method. See CAST.audit for an SRS audit method.

Examples

# The reported poll data: make an elec.data object for processing
data(santa.cruz)
Z = elec.data(santa.cruz, C.names=c("leopold","danner"))
Z

# Make a plan
plan = tri.calc.sample( Z, beta=0.75, guess.N = 10, p_d = 0.05,
               swing=10, power=0.9, bound="e.plus" )

# Conduct the audit
data(santa.cruz.audit)
res = trinomial.audit( Z, santa.cruz.audit )
res

# Compute the bound.  Everything is scaled by 100 (i.e. to percents) for easier numbers. 
trinomial.bound(n=res$n, k = res$k, d=100*plan$d, e.max=100, p.value.bound=100/plan$T,
           xlim=c(0.75,1), ylim=c(0.0,0.25),
           alpha.lvls=c(25), asp=1,
           main="Auditing Santa Cruz with Trinomial Bound" )