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Implement stratified and by-order sampling

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RunasSudo 2021-08-05 18:41:39 +10:00
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9 changed files with 344 additions and 99 deletions
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12
docs/options.md
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@ -95,8 +95,6 @@ Random sample methods are also supported, but also not recommended:
The use of a random sample method requires *Normalise ballots* to be enabled, and will usually be used with a *Quota criterion* set to *>=*.
In both random sample methods, the subset is selected using the deterministic method used in [Cambridge, Massachusetts](https://web.archive.org/web/20081118104049/http://www.fairvote.org/media/1993countmanual.pdf) (derived from Article IX of the former 1938 Cincinnati *Code of Ordinances*). This depends on the order of ballot papers in the BLT file, and is independent of the *Random seed* option.
### Papers to examine in surplus transfer (--t ransferable-only)
* *Include non-transferable papers* (default): When this option is selected, all ballot papers of the transferring candidate are examined. Non-transferable papers are always exhausted at the relevant surplus fractions.
@ -119,6 +117,16 @@ When *Surplus method* is set to *Meek method*, this option controls how candidat
* When NZ-style exclusion is disabled (default), the excluded candidate's keep value is immediately reduced to 0. This is the method specified in the 1987 and 2006 Meek rules.
* When NZ-style exclusion is enabled, all elected candidates' keep values are first updated by one further iteration; only then is the excluded candidate's keep value reduced to 0. This is the method specified in the New Zealand *Local Electoral Regulations 2001*.
### (Sample) Sample method (--sample)
When *Surplus method* is set to a random sample method, this option controls which subset of ballot papers is selected for transfer during surplus distributions:
* *Stratified (then by order)*: The candidate's ballot papers are first stratified into subparcels according to next available preference. From each subparcel, the subset transferred comprises the ballot papers most recently received by the candidate.
* *By order*: The subset transferred comprises the ballot papers most recently received by the candidate.
* *Every n-th ballot*: The subset is selected using the deterministic method used in [Cambridge, Massachusetts](https://web.archive.org/web/20081118104049/http://www.fairvote.org/media/1993countmanual.pdf) (derived from Article IX of the former 1938 Cincinnati *Code of Ordinances*).
In any case, the subset selected depends on the order of ballot papers in the BLT file, and is independent of the *Random seed* option.
### (Sample) Transfer ballot-by-ballot (--sample-per-ballot)
When *Surplus method* is set to a random sample method, this option controls when candidates are declared elected:

10
html/index.html
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@ -141,9 +141,17 @@
</label>
</div>
<div>
<label style="margin-right:1em;">
<span class="pill-grey" title="This option has effect only if “Method” is set to a random sample method">Sample</span>
Sample method:
<select id="selSample">
<option value="stratified" selected>Stratified (then by order)</option>
<option value="by_order">By order</option>
<option value="nth_ballot">Every n-th ballot</option>
</select>
</label>
<label>
<input type="checkbox" id="chkSamplePerBallot">
<span class="pill-grey" title="This option has effect only if “Method” is set to a sample-based method">Sample</span>
Per-ballot transfers
</label>
</div>

2
html/index.js
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@ -149,6 +149,7 @@ async function clickCount() {
document.getElementById('selPapers').value == 'transferable',
document.getElementById('selExclusion').value,
document.getElementById('chkMeekNZExclusion').checked,
document.getElementById('selSample').value,
document.getElementById('chkSamplePerBallot').checked,
document.getElementById('chkBulkElection').checked,
document.getElementById('chkBulkExclusion').checked,
@ -566,6 +567,7 @@ function changePreset() {
document.getElementById('chkBulkElection').checked = true;
document.getElementById('chkBulkExclusion').checked = false;
document.getElementById('chkDeferSurpluses').checked = false;
document.getElementById('selSample').value = 'nth_ballot';
document.getElementById('chkSamplePerBallot').checked = true;
document.getElementById('txtMinThreshold').value = '49';
document.getElementById('selNumbers').value = 'rational';

5
src/main.rs
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@ -139,6 +139,10 @@ struct STV {
#[clap(help_heading=Some("STV VARIANTS"), long)]
meek_nz_exclusion: bool,
/// (Cincinnati/Hare) Method of drawing a sample
#[clap(help_heading=Some("STV VARIANTS"), long, possible_values=&["stratified", "by_order", "nth_ballot"], default_value="stratified", value_name="method")]
sample: String,
/// (Cincinnati/Hare) Sample-based methods: Check for candidate election after each individual ballot paper transfer
#[clap(help_heading=Some("STV VARIANTS"), long)]
sample_per_ballot: bool,
@ -278,6 +282,7 @@ where
cmd_opts.transferable_only,
cmd_opts.exclusion.into(),
cmd_opts.meek_nz_exclusion,
cmd_opts.sample.into(),
cmd_opts.sample_per_ballot,
!cmd_opts.no_early_bulk_elect,
cmd_opts.bulk_exclude,

11
src/stv/gregory.rs
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@ -115,7 +115,9 @@ where
return Ok(false);
}
/// Return the denominator of the transfer value
/// Return the denominator of the surplus fraction
///
/// Returns `None` if the value of transferable votes <= surplus (i.e. all transferable votes are transferred at values received)
fn calculate_surplus_denom<N: Number>(surplus: &N, result: &NextPreferencesResult<N>, transferable_votes: &N, weighted: bool, transferable_only: bool) -> Option<N>
where
for<'r> &'r N: ops::Sub<&'r N, Output=N>
@ -295,10 +297,11 @@ where
None => {
surplus_fraction = None;
if opts.transferable_only {
state.logger.log_literal(format!("Transferring {:.0} transferable ballots, totalling {:.dps$} transferable votes, at values received.", &result.total_ballots - &result.exhausted.num_ballots, transferable_votes, dps=opts.pp_decimals));
// This can only happen if --transferable-only
if &result.total_ballots - &result.exhausted.num_ballots == N::one() {
state.logger.log_literal(format!("Transferring 1 transferable ballot, totalling {:.dps$} transferable votes, at values received.", transferable_votes, dps=opts.pp_decimals));
} else {
state.logger.log_literal(format!("Transferring {:.0} ballots, totalling {:.dps$} votes, at values received.", result.total_ballots, result.total_votes, dps=opts.pp_decimals));
state.logger.log_literal(format!("Transferring {:.0} transferable ballots, totalling {:.dps$} transferable votes, at values received.", &result.total_ballots - &result.exhausted.num_ballots, transferable_votes, dps=opts.pp_decimals));
}
}
}

51
src/stv/mod.rs
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@ -21,7 +21,7 @@
pub mod gregory;
/// Meek method of surplus distributions, etc.
pub mod meek;
/// Random subset methods of surplus distributions
/// Random sample methods of surplus distributions
pub mod sample;
/// WebAssembly wrappers
@ -110,6 +110,10 @@ pub struct STVOptions {
#[builder(default="false")]
pub meek_nz_exclusion: bool,
/// (Cincinnati/Hare) Method of drawing a sample
#[builder(default="SampleMethod::Stratified")]
pub sample: SampleMethod,
/// (Cincinnati/Hare) Sample-based methods: Check for candidate election after each individual ballot paper transfer
#[builder(default="false")]
pub sample_per_ballot: bool,
@ -182,6 +186,7 @@ impl STVOptions {
if self.exclusion != ExclusionMethod::SingleStage { flags.push(self.exclusion.describe()); }
}
if self.surplus == SurplusMethod::Meek && self.meek_nz_exclusion { flags.push("--meek-nz-exclusion".to_string()); }
if (self.surplus == SurplusMethod::Cincinnati || self.surplus == SurplusMethod::Hare) && self.sample != SampleMethod::Stratified { flags.push(self.sample.describe()); }
if (self.surplus == SurplusMethod::Cincinnati || self.surplus == SurplusMethod::Hare) && self.sample_per_ballot { flags.push("--sample-per-ballot".to_string()); }
if !self.early_bulk_elect { flags.push("--no-early-bulk-elect".to_string()); }
if self.bulk_exclude { flags.push("--bulk-exclude".to_string()); }
@ -207,6 +212,7 @@ impl STVOptions {
if self.surplus == SurplusMethod::Cincinnati || self.surplus == SurplusMethod::Hare {
if self.round_quota != Some(0) { return Err(STVError::InvalidOptions("--surplus cincinnati and --surplus hare require --round-quota 0")); }
if !self.normalise_ballots { return Err(STVError::InvalidOptions("--surplus cincinnati and --surplus hare require --normalise-ballots")); }
if self.sample == SampleMethod::Stratified && self.sample_per_ballot { return Err(STVError::InvalidOptions("--sample stratified is incompatible with --sample-per-ballot")); }
}
if self.min_threshold != "0" && self.defer_surpluses { return Err(STVError::InvalidOptions("--min-threshold is incompatible with --defer-surpluses")); } // TODO: Permit this
return Ok(());
@ -474,6 +480,41 @@ impl<S: AsRef<str>> From<S> for ExclusionMethod {
}
}
/// Enum of options for [STVOptions::sample]
#[wasm_bindgen]
#[derive(Clone, Copy)]
#[derive(PartialEq)]
pub enum SampleMethod {
/// Stratify the ballots into parcels according to next available preference and transfer the last ballots from each parcel
Stratified,
/// Transfer the last ballots
ByOrder,
/// Transfer every n-th ballot, Cincinnati style
NthBallot,
}
impl SampleMethod {
/// Convert to CLI argument representation
fn describe(self) -> String {
match self {
SampleMethod::Stratified => "--sample stratified",
SampleMethod::ByOrder => "--sample by_order",
SampleMethod::NthBallot => "--sample nth_ballot",
}.to_string()
}
}
impl<S: AsRef<str>> From<S> for SampleMethod {
fn from(s: S) -> Self {
match s.as_ref() {
"stratified" => SampleMethod::Stratified,
"by_order" => SampleMethod::ByOrder,
"nth_ballot" => SampleMethod::NthBallot,
_ => panic!("Invalid --sample-method"),
}
}
}
/// Enum of options for [STVOptions::constraint_mode]
#[derive(Clone, Copy)]
#[derive(PartialEq)]
@ -1257,9 +1298,13 @@ where
{
let mut excluded_candidates: Vec<&Candidate> = Vec::new();
// Exclude candidates below min threshold
if state.num_excluded == 0 {
excluded_candidates = hopefuls_below_threshold(state, opts);
if opts.bulk_exclude && opts.min_threshold == "0" {
// Proceed directly to bulk exclusion, as candidates with 0 votes will necessarily be included
} else {
// Exclude candidates below min threshold
excluded_candidates = hopefuls_below_threshold(state, opts);
}
}
// Attempt a bulk exclusion

341
src/stv/sample.rs
View File

@ -18,12 +18,31 @@
use crate::constraints;
use crate::election::{Candidate, CandidateState, CountState, Parcel, Vote};
use crate::numbers::Number;
use crate::stv::{STVOptions, SurplusMethod};
use crate::stv::{STVOptions, SampleMethod, SurplusMethod};
use std::cmp::max;
use std::collections::HashMap;
use std::ops;
use super::STVError;
use super::{NextPreferencesResult, STVError};
/// Return the denominator of the surplus fraction
///
/// Returns `None` if transferable ballots <= surplus (i.e. all transferable ballots are transferred at full value)
fn calculate_surplus_denom<N: Number>(surplus: &N, result: &NextPreferencesResult<N>, transferable_ballots: &N, transferable_only: bool) -> Option<N>
where
for<'r> &'r N: ops::Sub<&'r N, Output=N>
{
if transferable_only {
if transferable_ballots > surplus {
return Some(transferable_ballots.clone());
} else {
return None;
}
} else {
return Some(result.total_ballots.clone());
}
}
/// Distribute the surplus of a given candidate according to the random subset method, based on [STVOptions::surplus]
pub fn distribute_surplus<N: Number>(state: &mut CountState<N>, opts: &STVOptions, elected_candidate: &Candidate) -> Result<(), STVError>
@ -39,7 +58,7 @@ where
let count_card = state.candidates.get_mut(elected_candidate).unwrap();
let surplus = &count_card.votes - state.quota.as_ref().unwrap();
let votes;
let mut votes;
match opts.surplus {
SurplusMethod::Cincinnati => {
// Inclusive
@ -53,49 +72,250 @@ where
_ => unreachable!()
}
// Calculate skip value
let total_ballots = votes.len();
let mut skip_fraction = N::from(total_ballots) / &surplus;
skip_fraction.round_mut(0);
match opts.sample {
SampleMethod::Stratified => {
// Stratified by next available preference
// FIXME: This is untested
state.logger.log_literal(format!("Examining {:.0} ballots, with skip value {:.0}.", total_ballots, skip_fraction));
let result = super::next_preferences(state, votes);
// Number the votes
let mut numbered_votes: HashMap<usize, Vote<N>> = HashMap::new();
for (i, vote) in votes.into_iter().enumerate() {
numbered_votes.insert(i, vote);
let transferable_ballots = &result.total_ballots - &result.exhausted.num_ballots;
let surplus_denom = calculate_surplus_denom(&surplus, &result, &transferable_ballots, opts.transferable_only);
let mut surplus_fraction;
match surplus_denom {
Some(v) => {
surplus_fraction = Some(surplus.clone() / v);
// Round down if requested
if let Some(dps) = opts.round_surplus_fractions {
surplus_fraction.as_mut().unwrap().floor_mut(dps);
}
if opts.transferable_only {
if &result.total_ballots - &result.exhausted.num_ballots == N::one() {
state.logger.log_literal(format!("Examining 1 transferable ballot, with surplus fraction {:.dps2$}.", surplus_fraction.as_ref().unwrap(), dps2=max(opts.pp_decimals, 2)));
} else {
state.logger.log_literal(format!("Examining {:.0} transferable ballots, with surplus fraction {:.dps2$}.", &result.total_ballots - &result.exhausted.num_ballots, surplus_fraction.as_ref().unwrap(), dps2=max(opts.pp_decimals, 2)));
}
} else {
if result.total_ballots == N::one() {
state.logger.log_literal(format!("Examining 1 ballot, with surplus fraction {:.dps2$}.", surplus_fraction.as_ref().unwrap(), dps2=max(opts.pp_decimals, 2)));
} else {
state.logger.log_literal(format!("Examining {:.0} ballots, with surplus fraction {:.dps2$}.", result.total_ballots, surplus_fraction.as_ref().unwrap(), dps2=max(opts.pp_decimals, 2)));
}
}
}
None => {
surplus_fraction = None;
// This can only happen if --transferable-only
if result.total_ballots == N::one() {
state.logger.log_literal("Transferring 1 ballot at full value.".to_string());
} else {
state.logger.log_literal(format!("Transferring {:.0} ballots at full value.", result.total_ballots));
}
}
}
let mut checksum = N::new();
for (candidate, entry) in result.candidates.into_iter() {
// Credit transferred votes
let mut candidate_transfers;
match surplus_fraction {
Some(ref f) => {
candidate_transfers = entry.num_ballots * f;
candidate_transfers.floor_mut(0);
}
None => {
// All ballots transferred
candidate_transfers = entry.num_ballots.clone();
}
}
let candidate_transfers_usize: usize = format!("{:.0}", candidate_transfers).parse().expect("Transfers overflow usize");
let count_card = state.candidates.get_mut(candidate).unwrap();
count_card.transfer(&candidate_transfers);
checksum += candidate_transfers;
let parcel = Parcel {
votes: entry.votes.into_iter().rev().take(candidate_transfers_usize).rev().collect(),
source_order: state.num_elected + state.num_excluded,
};
count_card.parcels.push(parcel);
}
// Credit exhausted votes
let mut exhausted_transfers;
if opts.transferable_only {
if transferable_ballots > surplus {
// No ballots exhaust
exhausted_transfers = N::new();
} else {
exhausted_transfers = &surplus - &transferable_ballots;
if let Some(dps) = opts.round_votes {
exhausted_transfers.floor_mut(dps);
}
}
} else {
exhausted_transfers = result.exhausted.num_ballots * surplus_fraction.as_ref().unwrap();
exhausted_transfers.floor_mut(0);
}
let exhausted_transfers_usize: usize = format!("{:.0}", exhausted_transfers).parse().expect("Transfers overflow usize");
state.exhausted.transfer(&exhausted_transfers);
checksum += exhausted_transfers;
// Transfer exhausted votes
let parcel = Parcel {
votes: result.exhausted.votes.into_iter().rev().take(exhausted_transfers_usize).rev().collect(),
source_order: state.num_elected + state.num_excluded,
};
state.exhausted.parcels.push(parcel);
// Finalise candidate votes
let count_card = state.candidates.get_mut(elected_candidate).unwrap();
count_card.transfers = -&surplus;
count_card.votes.assign(state.quota.as_ref().unwrap());
checksum -= surplus;
count_card.parcels.clear(); // Mark surpluses as done
// Update loss by fraction
state.loss_fraction.transfer(&-checksum);
}
SampleMethod::ByOrder => {
// Ballots by order
// FIXME: This is untested
state.logger.log_literal(format!("Examining {:.0} ballots.", votes.len())); // votes.len() is total ballots as --normalise-ballots is required
// Transfer candidate votes
while &state.candidates[elected_candidate].votes > state.quota.as_ref().unwrap() {
match votes.pop() {
Some(vote) => {
// Transfer to next preference
transfer_ballot(state, opts, elected_candidate, vote)?;
}
None => {
// We have run out of ballot papers
// Remaining ballot papers exhaust
let surplus = &state.candidates[elected_candidate].votes - state.quota.as_ref().unwrap();
state.exhausted.transfer(&surplus);
state.candidates.get_mut(elected_candidate).unwrap().transfer(&-surplus);
}
}
}
}
SampleMethod::NthBallot => {
// Every nth-ballot (Cincinnati-style)
// Calculate skip value
let total_ballots = votes.len();
let mut skip_fraction = N::from(total_ballots) / &surplus;
skip_fraction.round_mut(0);
state.logger.log_literal(format!("Examining {:.0} ballots, with skip value {:.0}.", total_ballots, skip_fraction));
// Number the votes
let mut numbered_votes: HashMap<usize, Vote<N>> = HashMap::new();
for (i, vote) in votes.into_iter().enumerate() {
numbered_votes.insert(i, vote);
}
// Transfer candidate votes
let skip_value: usize = format!("{:.0}", skip_fraction).parse().expect("Skip value overflows usize");
let mut iteration = 0;
let mut index = skip_value - 1; // Subtract 1 as votes are 0-indexed
while &state.candidates[elected_candidate].votes > state.quota.as_ref().unwrap() {
// Transfer one vote to next available preference
let vote = numbered_votes.remove(&index).unwrap();
transfer_ballot(state, opts, elected_candidate, vote)?;
index += skip_value;
if index >= total_ballots {
iteration += 1;
index = iteration + skip_value - 1;
if iteration >= skip_value {
// We have run out of ballot papers
// Remaining ballot papers exhaust
let surplus = &state.candidates[elected_candidate].votes - state.quota.as_ref().unwrap();
state.exhausted.transfer(&surplus);
state.candidates.get_mut(elected_candidate).unwrap().transfer(&-surplus);
break;
}
}
}
}
}
// Transfer candidate votes
let skip_value: usize = format!("{:.0}", skip_fraction).parse().expect("Skip value overflows usize");
let mut iteration = 0;
let mut index = skip_value - 1; // Subtract 1 as votes are 0-indexed
return Ok(());
}
while &state.candidates[elected_candidate].votes > state.quota.as_ref().unwrap() {
let mut vote = numbered_votes.remove(&index).unwrap();
/// Transfer the given ballot paper to its next available preference, and check for candidates meeting the quota if --sample-per-ballot
///
/// Does nothing if --transferable-only and the ballot is nontransferable.
fn transfer_ballot<'a, N: Number>(state: &mut CountState<'a, N>, opts: &STVOptions, elected_candidate: &Candidate, mut vote: Vote<'a, N>) -> Result<(), STVError> {
// Get next preference
let mut next_candidate = None;
for (i, preference) in vote.ballot.preferences.iter().enumerate().skip(vote.up_to_pref) {
let candidate = &state.election.candidates[*preference];
let count_card = &state.candidates[candidate];
// Transfer to next preference
let mut next_candidate = None;
for (i, preference) in vote.ballot.preferences.iter().enumerate().skip(vote.up_to_pref) {
let candidate = &state.election.candidates[*preference];
let count_card = &state.candidates[candidate];
if let CandidateState::Hopeful | CandidateState::Guarded = count_card.state {
next_candidate = Some(candidate);
vote.up_to_pref = i + 1;
break;
}
}
if let CandidateState::Hopeful | CandidateState::Guarded = count_card.state {
next_candidate = Some(candidate);
vote.up_to_pref = i + 1;
break;
// Have to structure like this to satisfy Rust's borrow checker
if let Some(candidate) = next_candidate {
// Available preference
state.candidates.get_mut(elected_candidate).unwrap().transfer(&-vote.value.clone());
let count_card = state.candidates.get_mut(candidate).unwrap();
count_card.transfer(&vote.value);
match count_card.parcels.last_mut() {
Some(parcel) => {
if parcel.source_order == state.num_elected + state.num_excluded {
parcel.votes.push(vote);
} else {
let parcel = Parcel {
votes: vec![vote],
source_order: state.num_elected + state.num_excluded,
};
count_card.parcels.push(parcel);
}
}
None => {
let parcel = Parcel {
votes: vec![vote],
source_order: state.num_elected + state.num_excluded,
};
count_card.parcels.push(parcel);
}
}
// Have to structure like this to satisfy Rust's borrow checker
if let Some(candidate) = next_candidate {
// Available preference
if opts.sample_per_ballot {
super::elect_hopefuls(state, opts)?;
}
} else {
// Exhausted
if opts.transferable_only {
// Another ballot paper required
} else {
state.candidates.get_mut(elected_candidate).unwrap().transfer(&-vote.value.clone());
state.exhausted.transfer(&vote.value);
let count_card = state.candidates.get_mut(candidate).unwrap();
count_card.transfer(&vote.value);
match count_card.parcels.last_mut() {
match state.exhausted.parcels.last_mut() {
Some(parcel) => {
if parcel.source_order == state.num_elected + state.num_excluded {
parcel.votes.push(vote);
@ -104,7 +324,7 @@ where
votes: vec![vote],
source_order: state.num_elected + state.num_excluded,
};
count_card.parcels.push(parcel);
state.exhausted.parcels.push(parcel);
}
}
None => {
@ -112,58 +332,9 @@ where
votes: vec![vote],
source_order: state.num_elected + state.num_excluded,
};
count_card.parcels.push(parcel);
state.exhausted.parcels.push(parcel);
}
}
if opts.sample_per_ballot {
super::elect_hopefuls(state, opts)?;
}
} else {
// Exhausted
if opts.transferable_only {
// Another ballot paper required
} else {
state.candidates.get_mut(elected_candidate).unwrap().transfer(&-vote.value.clone());
state.exhausted.transfer(&vote.value);
match state.exhausted.parcels.last_mut() {
Some(parcel) => {
if parcel.source_order == state.num_elected + state.num_excluded {
parcel.votes.push(vote);
} else {
let parcel = Parcel {
votes: vec![vote],
source_order: state.num_elected + state.num_excluded,
};
state.exhausted.parcels.push(parcel);
}
}
None => {
let parcel = Parcel {
votes: vec![vote],
source_order: state.num_elected + state.num_excluded,
};
state.exhausted.parcels.push(parcel);
}
}
}
}
index += skip_value;
if index >= total_ballots {
iteration += 1;
index = iteration + skip_value - 1;
if iteration >= skip_value {
// We have run out of ballot papers
// Remaining ballot papers exhaust
let surplus = &state.candidates[elected_candidate].votes - state.quota.as_ref().unwrap();
state.exhausted.transfer(&surplus);
state.candidates.get_mut(elected_candidate).unwrap().transfer(&-surplus);
break;
}
}
}

2
src/stv/wasm.rs
View File

@ -229,6 +229,7 @@ impl STVOptions {
transferable_only: bool,
exclusion: &str,
meek_nz_exclusion: bool,
sample: &str,
sample_per_ballot: bool,
early_bulk_elect: bool,
bulk_exclude: bool,
@ -256,6 +257,7 @@ impl STVOptions {
transferable_only,
exclusion.into(),
meek_nz_exclusion,
sample.into(),
sample_per_ballot,
early_bulk_elect,
bulk_exclude,

1
tests/cambridge.rs
View File

@ -29,6 +29,7 @@ fn cambridge_cc03_rational() {
.quota_criterion(stv::QuotaCriterion::GreaterOrEqual)
.surplus(stv::SurplusMethod::Cincinnati)
.transferable_only(true)
.sample(stv::SampleMethod::NthBallot)
.sample_per_ballot(true)
.early_bulk_elect(false)
.min_threshold("49".to_string())