redist_mergesplit uses a Markov Chain Monte Carlo algorithm to generate congressional or legislative redistricting plans according to contiguity, population, compactness, and administrative boundary constraints. The MCMC proposal is the same as is used in the SMC sampler; it is similar but not identical to those used in the references. 1-level hierarchical Merge-split is supported through the counties parameter; unlike in the SMC algorithm, this does not guarantee a maximum number of county splits.

redist_mergesplit(
map,
nsims,
warmup = floor(nsims/2),
init_plan = NULL,
counties = NULL,
compactness = 1,
constraints = list(),
constraint_fn = function(m) rep(0, ncol(m)),
k = NULL,
init_name = NULL,
verbose = TRUE,
silent = FALSE
)

redist.mergesplit(
total_pop,
nsims,
ndists,
pop_tol = 0.01,
init_plan,
counties,
compactness = 1,
constraints = list(),
constraint_fn = function(m) rep(0, ncol(m)),
k = NULL,
verbose = TRUE,
silent = FALSE
)

## Arguments

map A redist_map object. The number of samples to draw, including warmup. The number of warmup samples to discard. The initial state of the map. If not provided, will default to the reference map of the map object, or if none exists, will sample a random initial state using redist_smc. You can also request a random initial state by setting init_plan="sample". A vector containing county (or other administrative or geographic unit) labels for each unit, which may be integers ranging from 1 to the number of counties, or a factor or character vector. If provided, the algorithm will generate maps tend to follow county lines. You may combine this with a Gibbs constraint on the number of county splits using the constraints parameter; see below. If no county-split considerations are desired, this parameter should be left blank. Controls the compactness of the generated districts, with higher values preferring more compact districts. Must be nonnegative. See the 'Details' section for more information, and computational considerations. A list containing information on constraints to implement. See the 'Details' section for more information. A function which takes in a matrix where each column is a redistricting plan and outputs a vector of log-weights, which will be added the the final weights. The threshold value used in the heuristic to select a value k_i for each splitting iteration. Set to 0.9999 or 1 if the algorithm does not appear to be sampling from the target distribution. Must be between 0 and 1. The number of edges to consider cutting after drawing a spanning tree. Should be selected automatically in nearly all cases. a name for the initial plan, or FALSE to not include the initial plan in the output. Defaults to the column name of the existing plan, or "" if the initial plan is sampled. Whether to print out intermediate information while sampling. Recommended. Whether to suppress all diagnostic information. adjacency matrix, list, or object of class "SpatialPolygonsDataFrame." A vector containing the populations of each geographic unit The number of congressional districts. The desired population constraint. All sampled districts will have a deviation from the target district size no more than this value in percentage terms, i.e., pop_tol=0.01 will ensure districts have populations within 1% of the target population.

## Value

redist_mergesplit returns an object of class redist_plans containing the simulated plans.

redist.mergesplit (Deprecated) returns an object of class list containing the simulated plans.

## Details

This function draws samples from a specific target measure, controlled by the compactness, constraints, and constraint_fn parameters.

Higher values of compactness sample more compact districts; setting this parameter to 1 is computationally efficient and generates nicely compact districts.

The constraints parameter allows the user to apply several common redistricting constraints without implementing them by hand. This parameter is a list, which may contain any of the following named entries:

• status_quo: a list with two entries:

• strength, a number controlling the tendency of the generated districts to respect the status quo, with higher values preferring more similar districts.

• current, a vector containing district assignments for the current map.

• hinge: a list with three entries:

• strength, a number controlling the strength of the Voting Rights Act (VRA) constraint, with higher values prioritizing majority-minority districts over other considerations.

• tgts_min, the target percentage(s) of minority voters in minority opportunity districts. Defaults to c(0.55).

• min_pop, A vector containing the minority population of each geographic unit.

• incumbency: a list with two entries:

• strength, a number controlling the tendency of the generated districts to avoid pairing up incumbents.

• incumbents, a vector of precinct indices, one for each incumbent's home address.

• splits: a list with one entry:

• strength, a number controlling the tendency of the generated districts to avoid splitting counties.

• multisplits: a list with one entry:

• strength, a number controlling the tendency of the generated districts to avoid splitting counties multiple times.

• vra: a list with five entries, which may be set up using redist.constraint.helper:

• strength, a number controlling the strength of the Voting Rights Act (VRA) constraint, with higher values prioritizing majority-minority districts over other considerations.

• tgt_vra_min, the target percentage of minority voters in minority opportunity districts. Defaults to 0.55.

• tgt_vra_other The target percentage of minority voters in other districts. Defaults to 0.25, but should be set to reflect the total minority population in the state.

• pow_vra, which controls the allowed deviation from the target minority percentage; higher values are more tolerant. Defaults to 1.5

• min_pop, A vector containing the minority population of each geographic unit.

All constraints are fed into a Gibbs measure, with coefficients on each constraint set by the corresponding strength parameters. The strength can be any real number, with zero corresponding to no constraint. The status_quo constraint adds a term measuring the variation of information distance between the plan and the reference, rescaled to [0, 1]. The hinge constraint takes a list of target minority percentages. It matches each district to its nearest target percentage, and then applies a penalty of the form $$\sqrt{max(0, tgt - minpct)}$$, summing across districts. This penalizes districts which are below their target population. The incumbency constraint adds a term counting the number of districts containing paired-up incumbents. The splits constraint adds a term counting the number of counties which contain precincts belonging to more than one district. The vra constraint (not recommended) adds a term of the form $$(|tgtvramin-minpct||tgtvraother-minpct|)^{powvra})$$, which encourages districts to have minority percentages near either tgt_vra_min or tgt_vra_other. This can be visualized with redist.plot.penalty.

## References

Carter, D., Herschlag, G., Hunter, Z., and Mattingly, J. (2019). A merge-split proposal for reversible Monte Carlo Markov chain sampling of redistricting plans. arXiv preprint arXiv:1911.01503.

DeFord, D., Duchin, M., and Solomon, J. (2019). Recombination: A family of Markov chains for redistricting. arXiv preprint arXiv:1911.05725.

## Examples

# \donttest{
data(fl25)

fl_map = redist_map(fl25, ndists=3, pop_tol=0.1)
#> Projecting to CRS 3857
sampled_basic = redist_mergesplit(fl_map, 10000)
#> MARKOV CHAIN MONTE CARLO
#> Sampling 10000 25-unit maps with 3 districts and population between 52512.9 and 64182.4.
#> Using k = 2
#> Iteration 500/10000
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#> Iteration 10000/10000
#> Acceptance rate: 76.96
sampled_constr = redist_mergesplit(fl_map, 10000, constraints=list(
incumbency = list(strength=1000, incumbents=c(3, 6, 25))
))
#> MARKOV CHAIN MONTE CARLO
#> Sampling 10000 25-unit maps with 3 districts and population between 52512.9 and 64182.4.
#> Using k = 3
#> Iteration 500/10000
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#> Acceptance rate: 83.46# }