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// This file is part of Substrate. // Copyright (C) 2019-2020 Parity Technologies (UK) Ltd. // SPDX-License-Identifier: Apache-2.0 // Licensed under the Apache License, Version 2.0 (the "License"); // you may not use this file except in compliance with the License. // You may obtain a copy of the License at // // http://www.apache.org/licenses/LICENSE-2.0 // // Unless required by applicable law or agreed to in writing, software // distributed under the License is distributed on an "AS IS" BASIS, // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. // See the License for the specific language governing permissions and // limitations under the License. //! A set of election algorithms to be used with a substrate runtime, typically within the staking //! sub-system. Notable implementation include //! //! - [`seq_phragmen`]: Implements the Phragmén Sequential Method. An un-ranked, relatively fast //! election method that ensures PJR, but does not provide a constant factor approximation of the //! maximin problem. //! - [`balance_solution`]: Implements the star balancing algorithm. This iterative process can //! increase a solutions score, as described in [`evaluate_support`]. //! //! More information can be found at: https://arxiv.org/abs/2004.12990 #![cfg_attr(not(feature = "std"), no_std)] use sp_std::{prelude::*, collections::btree_map::BTreeMap, fmt::Debug, cmp::Ordering, convert::TryFrom}; use sp_arithmetic::{ PerThing, Rational128, ThresholdOrd, InnerOf, Normalizable, helpers_128bit::multiply_by_rational, traits::{Zero, Saturating, Bounded, SaturatedConversion}, }; #[cfg(test)] mod mock; #[cfg(test)] mod tests; #[cfg(feature = "std")] use serde::{Serialize, Deserialize}; #[cfg(feature = "std")] use codec::{Encode, Decode}; mod node; mod reduce; mod helpers; // re-export reduce stuff. pub use reduce::reduce; // re-export the helpers. pub use helpers::*; // re-export the compact macro, with the dependencies of the macro. #[doc(hidden)] pub use codec; #[doc(hidden)] pub use sp_arithmetic; /// Simple Extension trait to easily convert `None` from index closures to `Err`. /// /// This is only generated and re-exported for the compact solution code to use. #[doc(hidden)] pub trait __OrInvalidIndex<T> { fn or_invalid_index(self) -> Result<T, Error>; } impl<T> __OrInvalidIndex<T> for Option<T> { fn or_invalid_index(self) -> Result<T, Error> { self.ok_or(Error::CompactInvalidIndex) } } // re-export the compact solution type. pub use sp_npos_elections_compact::generate_solution_type; /// A trait to limit the number of votes per voter. The generated compact type will implement this. pub trait VotingLimit { const LIMIT: usize; } /// an aggregator trait for a generic type of a voter/target identifier. This usually maps to /// substrate's account id. pub trait IdentifierT: Clone + Eq + Default + Ord + Debug + codec::Codec {} impl<T: Clone + Eq + Default + Ord + Debug + codec::Codec> IdentifierT for T {} /// The errors that might occur in the this crate and compact. #[derive(Debug, Eq, PartialEq)] pub enum Error { /// While going from compact to staked, the stake of all the edges has gone above the /// total and the last stake cannot be assigned. CompactStakeOverflow, /// The compact type has a voter who's number of targets is out of bound. CompactTargetOverflow, /// One of the index functions returned none. CompactInvalidIndex, /// An error occurred in some arithmetic operation. ArithmeticError(&'static str), } /// A type which is used in the API of this crate as a numeric weight of a vote, most often the /// stake of the voter. It is always converted to [`ExtendedBalance`] for computation. pub type VoteWeight = u64; /// A type in which performing operations on vote weights are safe. pub type ExtendedBalance = u128; /// The score of an assignment. This can be computed from the support map via [`evaluate_support`]. pub type ElectionScore = [ExtendedBalance; 3]; /// A winner, with their respective approval stake. pub type WithApprovalOf<A> = (A, ExtendedBalance); /// The denominator used for loads. Since votes are collected as u64, the smallest ratio that we /// might collect is `1/approval_stake` where approval stake is the sum of votes. Hence, some number /// bigger than u64::max_value() is needed. For maximum accuracy we simply use u128; const DEN: u128 = u128::max_value(); /// A candidate entity for the election. #[derive(Clone, Default, Debug)] struct Candidate<AccountId> { /// Identifier. who: AccountId, /// Intermediary value used to sort candidates. score: Rational128, /// Sum of the stake of this candidate based on received votes. approval_stake: ExtendedBalance, /// Flag for being elected. elected: bool, } /// A voter entity. #[derive(Clone, Default, Debug)] struct Voter<AccountId> { /// Identifier. who: AccountId, /// List of candidates proposed by this voter. edges: Vec<Edge<AccountId>>, /// The stake of this voter. budget: ExtendedBalance, /// Incremented each time a candidate that this voter voted for has been elected. load: Rational128, } /// A candidate being backed by a voter. #[derive(Clone, Default, Debug)] struct Edge<AccountId> { /// Identifier. who: AccountId, /// Load of this vote. load: Rational128, /// Index of the candidate stored in the 'candidates' vector. candidate_index: usize, } /// Final result of the election. #[derive(Debug)] pub struct ElectionResult<AccountId, T: PerThing> { /// Just winners zipped with their approval stake. Note that the approval stake is merely the /// sub of their received stake and could be used for very basic sorting and approval voting. pub winners: Vec<WithApprovalOf<AccountId>>, /// Individual assignments. for each tuple, the first elements is a voter and the second /// is the list of candidates that it supports. pub assignments: Vec<Assignment<AccountId, T>>, } /// A voter's stake assignment among a set of targets, represented as ratios. #[derive(Debug, Clone, Default)] #[cfg_attr(feature = "std", derive(PartialEq, Eq, Encode, Decode))] pub struct Assignment<AccountId, P: PerThing> { /// Voter's identifier. pub who: AccountId, /// The distribution of the voter's stake. pub distribution: Vec<(AccountId, P)>, } impl<AccountId: IdentifierT, P: PerThing> Assignment<AccountId, P> where ExtendedBalance: From<InnerOf<P>>, { /// Convert from a ratio assignment into one with absolute values aka. [`StakedAssignment`]. /// /// It needs `stake` which is the total budget of the voter. If `fill` is set to true, /// it _tries_ to ensure that all the potential rounding errors are compensated and the /// distribution's sum is exactly equal to the total budget, by adding or subtracting the /// remainder from the last distribution. /// /// If an edge ratio is [`Bounded::min_value()`], it is dropped. This edge can never mean /// anything useful. pub fn into_staked(self, stake: ExtendedBalance) -> StakedAssignment<AccountId> where P: sp_std::ops::Mul<ExtendedBalance, Output = ExtendedBalance>, { let distribution = self.distribution .into_iter() .filter_map(|(target, p)| { // if this ratio is zero, then skip it. if p.is_zero() { None } else { // NOTE: this mul impl will always round to the nearest number, so we might both // overflow and underflow. let distribution_stake = p * stake; Some((target, distribution_stake)) } }) .collect::<Vec<(AccountId, ExtendedBalance)>>(); StakedAssignment { who: self.who, distribution, } } /// Try and normalize this assignment. /// /// If `Ok(())` is returned, then the assignment MUST have been successfully normalized to 100%. pub fn try_normalize(&mut self) -> Result<(), &'static str> { self.distribution .iter() .map(|(_, p)| *p) .collect::<Vec<_>>() .normalize(P::one()) .map(|normalized_ratios| self.distribution .iter_mut() .zip(normalized_ratios) .for_each(|((_, old), corrected)| { *old = corrected; }) ) } } /// A voter's stake assignment among a set of targets, represented as absolute values in the scale /// of [`ExtendedBalance`]. #[derive(Debug, Clone, Default)] #[cfg_attr(feature = "std", derive(PartialEq, Eq, Encode, Decode))] pub struct StakedAssignment<AccountId> { /// Voter's identifier pub who: AccountId, /// The distribution of the voter's stake. pub distribution: Vec<(AccountId, ExtendedBalance)>, } impl<AccountId> StakedAssignment<AccountId> { /// Converts self into the normal [`Assignment`] type. /// /// If `fill` is set to true, it _tries_ to ensure that all the potential rounding errors are /// compensated and the distribution's sum is exactly equal to 100%, by adding or subtracting /// the remainder from the last distribution. /// /// NOTE: it is quite critical that this attempt always works. The data type returned here will /// potentially get used to create a compact type; a compact type requires sum of ratios to be /// less than 100% upon un-compacting. /// /// If an edge stake is so small that it cannot be represented in `T`, it is ignored. This edge /// can never be re-created and does not mean anything useful anymore. pub fn into_assignment<P: PerThing>(self) -> Assignment<AccountId, P> where ExtendedBalance: From<InnerOf<P>>, AccountId: IdentifierT, { let stake = self.total(); let distribution = self.distribution .into_iter() .filter_map(|(target, w)| { let per_thing = P::from_rational_approximation(w, stake); if per_thing == Bounded::min_value() { None } else { Some((target, per_thing)) } }) .collect::<Vec<(AccountId, P)>>(); Assignment { who: self.who, distribution, } } /// Try and normalize this assignment. /// /// If `Ok(())` is returned, then the assignment MUST have been successfully normalized to /// `stake`. /// /// NOTE: current implementation of `.normalize` is almost safe to `expect()` upon. The only /// error case is when the input cannot fit in `T`, or the sum of input cannot fit in `T`. /// Sadly, both of these are dependent upon the implementation of `VoteLimit`, i.e. the limit /// of edges per voter which is enforced from upstream. Hence, at this crate, we prefer /// returning a result and a use the name prefix `try_`. pub fn try_normalize(&mut self, stake: ExtendedBalance) -> Result<(), &'static str> { self.distribution .iter() .map(|(_, ref weight)| *weight) .collect::<Vec<_>>() .normalize(stake) .map(|normalized_weights| self.distribution .iter_mut() .zip(normalized_weights.into_iter()) .for_each(|((_, weight), corrected)| { *weight = corrected; }) ) } /// Get the total stake of this assignment (aka voter budget). pub fn total(&self) -> ExtendedBalance { self.distribution.iter().fold(Zero::zero(), |a, b| a.saturating_add(b.1)) } } /// A structure to demonstrate the election result from the perspective of the candidate, i.e. how /// much support each candidate is receiving. /// /// This complements the [`ElectionResult`] and is needed to run the balancing post-processing. /// /// This, at the current version, resembles the `Exposure` defined in the Staking pallet, yet /// they do not necessarily have to be the same. #[derive(Default, Debug)] #[cfg_attr(feature = "std", derive(Serialize, Deserialize, Eq, PartialEq))] pub struct Support<AccountId> { /// Total support. pub total: ExtendedBalance, /// Support from voters. pub voters: Vec<(AccountId, ExtendedBalance)>, } /// A linkage from a candidate and its [`Support`]. pub type SupportMap<A> = BTreeMap<A, Support<A>>; /// Perform election based on Phragmén algorithm. /// /// Returns an `Option` the set of winners and their detailed support ratio from each voter if /// enough candidates are provided. Returns `None` otherwise. /// /// * `candidate_count`: number of candidates to elect. /// * `minimum_candidate_count`: minimum number of candidates to elect. If less candidates exist, /// `None` is returned. /// * `initial_candidates`: candidates list to be elected from. /// * `initial_voters`: voters list. /// /// This function does not strip out candidates who do not have any backing stake. It is the /// responsibility of the caller to make sure only those candidates who have a sensible economic /// value are passed in. From the perspective of this function, a candidate can easily be among the /// winner with no backing stake. pub fn seq_phragmen<AccountId, R>( candidate_count: usize, minimum_candidate_count: usize, initial_candidates: Vec<AccountId>, initial_voters: Vec<(AccountId, VoteWeight, Vec<AccountId>)>, ) -> Option<ElectionResult<AccountId, R>> where AccountId: Default + Ord + Clone, R: PerThing, { // return structures let mut elected_candidates: Vec<(AccountId, ExtendedBalance)>; let mut assigned: Vec<Assignment<AccountId, R>>; // used to cache and access candidates index. let mut c_idx_cache = BTreeMap::<AccountId, usize>::new(); // voters list. let num_voters = initial_candidates.len() + initial_voters.len(); let mut voters: Vec<Voter<AccountId>> = Vec::with_capacity(num_voters); // Iterate once to create a cache of candidates indexes. This could be optimized by being // provided by the call site. let mut candidates = initial_candidates .into_iter() .enumerate() .map(|(idx, who)| { c_idx_cache.insert(who.clone(), idx); Candidate { who, ..Default::default() } }) .collect::<Vec<Candidate<AccountId>>>(); // early return if we don't have enough candidates if candidates.len() < minimum_candidate_count { return None; } // collect voters. use `c_idx_cache` for fast access and aggregate `approval_stake` of // candidates. voters.extend(initial_voters.into_iter().map(|(who, voter_stake, votes)| { let mut edges: Vec<Edge<AccountId>> = Vec::with_capacity(votes.len()); for v in votes { if edges.iter().any(|e| e.who == v) { // duplicate edge. continue; } if let Some(idx) = c_idx_cache.get(&v) { // This candidate is valid + already cached. candidates[*idx].approval_stake = candidates[*idx].approval_stake .saturating_add(voter_stake.into()); edges.push(Edge { who: v.clone(), candidate_index: *idx, ..Default::default() }); } // else {} would be wrong votes. We don't really care about it. } Voter { who, edges: edges, budget: voter_stake.into(), load: Rational128::zero(), } })); // we have already checked that we have more candidates than minimum_candidate_count. let to_elect = candidate_count.min(candidates.len()); elected_candidates = Vec::with_capacity(candidate_count); assigned = Vec::with_capacity(candidate_count); // main election loop for _round in 0..to_elect { // loop 1: initialize score for c in &mut candidates { if !c.elected { // 1 / approval_stake == (DEN / approval_stake) / DEN. If approval_stake is zero, // then the ratio should be as large as possible, essentially `infinity`. if c.approval_stake.is_zero() { c.score = Rational128::from_unchecked(DEN, 0); } else { c.score = Rational128::from(DEN / c.approval_stake, DEN); } } } // loop 2: increment score for n in &voters { for e in &n.edges { let c = &mut candidates[e.candidate_index]; if !c.elected && !c.approval_stake.is_zero() { let temp_n = multiply_by_rational( n.load.n(), n.budget, c.approval_stake, ).unwrap_or_else(|_| Bounded::max_value()); let temp_d = n.load.d(); let temp = Rational128::from(temp_n, temp_d); c.score = c.score.lazy_saturating_add(temp); } } } // loop 3: find the best if let Some(winner) = candidates .iter_mut() .filter(|c| !c.elected) .min_by_key(|c| c.score) { // loop 3: update voter and edge load winner.elected = true; for n in &mut voters { for e in &mut n.edges { if e.who == winner.who { e.load = winner.score.lazy_saturating_sub(n.load); n.load = winner.score; } } } elected_candidates.push((winner.who.clone(), winner.approval_stake)); } else { break } } // end of all rounds // update backing stake of candidates and voters for n in &mut voters { let mut assignment = Assignment { who: n.who.clone(), ..Default::default() }; for e in &mut n.edges { if elected_candidates.iter().position(|(ref c, _)| *c == e.who).is_some() { let per_bill_parts: R::Inner = { if n.load == e.load { // Full support. No need to calculate. R::ACCURACY } else { if e.load.d() == n.load.d() { // return e.load / n.load. let desired_scale: u128 = R::ACCURACY.saturated_into(); let parts = multiply_by_rational( desired_scale, e.load.n(), n.load.n(), ) // If result cannot fit in u128. Not much we can do about it. .unwrap_or_else(|_| Bounded::max_value()); TryFrom::try_from(parts) // If the result cannot fit into R::Inner. Defensive only. This can // never happen. `desired_scale * e / n`, where `e / n < 1` always // yields a value smaller than `desired_scale`, which will fit into // R::Inner. .unwrap_or_else(|_| Bounded::max_value()) } else { // defensive only. Both edge and voter loads are built from // scores, hence MUST have the same denominator. Zero::zero() } } }; let per_thing = R::from_parts(per_bill_parts); assignment.distribution.push((e.who.clone(), per_thing)); } } let len = assignment.distribution.len(); if len > 0 { // To ensure an assertion indicating: no stake from the voter going to waste, // we add a minimal post-processing to equally assign all of the leftover stake ratios. let vote_count: R::Inner = len.saturated_into(); let accuracy = R::ACCURACY; let mut sum: R::Inner = Zero::zero(); assignment.distribution.iter().for_each(|a| sum = sum.saturating_add(a.1.deconstruct())); let diff = accuracy.saturating_sub(sum); let diff_per_vote = (diff / vote_count).min(accuracy); if !diff_per_vote.is_zero() { for i in 0..len { let current_ratio = assignment.distribution[i % len].1; let next_ratio = current_ratio .saturating_add(R::from_parts(diff_per_vote)); assignment.distribution[i % len].1 = next_ratio; } } // `remainder` is set to be less than maximum votes of a voter (currently 16). // safe to cast it to usize. let remainder = diff - diff_per_vote * vote_count; for i in 0..remainder.saturated_into::<usize>() { let current_ratio = assignment.distribution[i % len].1; let next_ratio = current_ratio.saturating_add(R::from_parts(1u8.into())); assignment.distribution[i % len].1 = next_ratio; } assigned.push(assignment); } } Some(ElectionResult { winners: elected_candidates, assignments: assigned, }) } /// Build the support map from the given election result. It maps a flat structure like /// /// ```nocompile /// assignments: vec![ /// voter1, vec![(candidate1, w11), (candidate2, w12)], /// voter2, vec![(candidate1, w21), (candidate2, w22)] /// ] /// ``` /// /// into a mapping of candidates and their respective support: /// /// ```nocompile /// SupportMap { /// candidate1: Support { /// own:0, /// total: w11 + w21, /// others: vec![(candidate1, w11), (candidate2, w21)] /// }, /// candidate2: Support { /// own:0, /// total: w12 + w22, /// others: vec![(candidate1, w12), (candidate2, w22)] /// }, /// } /// ``` /// /// The second returned flag indicates the number of edges who didn't corresponded to an actual /// winner from the given winner set. A value in this place larger than 0 indicates a potentially /// faulty assignment. /// /// `O(E)` where `E` is the total number of edges. pub fn build_support_map<AccountId>( winners: &[AccountId], assignments: &[StakedAssignment<AccountId>], ) -> (SupportMap<AccountId>, u32) where AccountId: Default + Ord + Clone, { let mut errors = 0; // Initialize the support of each candidate. let mut supports = <SupportMap<AccountId>>::new(); winners .iter() .for_each(|e| { supports.insert(e.clone(), Default::default()); }); // build support struct. for StakedAssignment { who, distribution } in assignments.iter() { for (c, weight_extended) in distribution.iter() { if let Some(support) = supports.get_mut(c) { support.total = support.total.saturating_add(*weight_extended); support.voters.push((who.clone(), *weight_extended)); } else { errors = errors.saturating_add(1); } } } (supports, errors) } /// Evaluate a support map. The returned tuple contains: /// /// - Minimum support. This value must be **maximized**. /// - Sum of all supports. This value must be **maximized**. /// - Sum of all supports squared. This value must be **minimized**. /// /// `O(E)` where `E` is the total number of edges. pub fn evaluate_support<AccountId>( support: &SupportMap<AccountId>, ) -> ElectionScore { let mut min_support = ExtendedBalance::max_value(); let mut sum: ExtendedBalance = Zero::zero(); // NOTE: The third element might saturate but fine for now since this will run on-chain and need // to be fast. let mut sum_squared: ExtendedBalance = Zero::zero(); for (_, support) in support.iter() { sum = sum.saturating_add(support.total); let squared = support.total.saturating_mul(support.total); sum_squared = sum_squared.saturating_add(squared); if support.total < min_support { min_support = support.total; } } [min_support, sum, sum_squared] } /// Compares two sets of election scores based on desirability and returns true if `this` is /// better than `that`. /// /// Evaluation is done in a lexicographic manner, and if each element of `this` is `that * epsilon` /// greater or less than `that`. /// /// Note that the third component should be minimized. pub fn is_score_better<P: PerThing>(this: ElectionScore, that: ElectionScore, epsilon: P) -> bool where ExtendedBalance: From<sp_arithmetic::InnerOf<P>> { match this .iter() .enumerate() .map(|(i, e)| ( e.ge(&that[i]), e.tcmp(&that[i], epsilon.mul_ceil(that[i])), )) .collect::<Vec<(bool, Ordering)>>() .as_slice() { // epsilon better in the score[0], accept. [(_, Ordering::Greater), _, _] => true, // less than epsilon better in score[0], but more than epsilon better in the second. [(true, Ordering::Equal), (_, Ordering::Greater), _] => true, // less than epsilon better in score[0, 1], but more than epsilon better in the third [(true, Ordering::Equal), (true, Ordering::Equal), (_, Ordering::Less)] => true, // anything else is not a good score. _ => false, } } /// Performs balancing post-processing to the output of the election algorithm. This happens in /// rounds. The number of rounds and the maximum diff-per-round tolerance can be tuned through input /// parameters. /// /// Returns the number of iterations that were preformed. /// /// - `assignments`: exactly the same as the output of [`seq_phragmen`]. /// - `supports`: mutable reference to s `SupportMap`. This parameter is updated. /// - `tolerance`: maximum difference that can occur before an early quite happens. /// - `iterations`: maximum number of iterations that will be processed. pub fn balance_solution<AccountId>( assignments: &mut Vec<StakedAssignment<AccountId>>, supports: &mut SupportMap<AccountId>, tolerance: ExtendedBalance, iterations: usize, ) -> usize where AccountId: Ord + Clone { if iterations == 0 { return 0; } let mut i = 0 ; loop { let mut max_diff = 0; for assignment in assignments.iter_mut() { let voter_budget = assignment.total(); let StakedAssignment { who, distribution } = assignment; let diff = do_balancing( who, voter_budget, distribution, supports, tolerance, ); if diff > max_diff { max_diff = diff; } } i += 1; if max_diff <= tolerance || i >= iterations { break i; } } } /// actually perform balancing. same interface is `balance_solution`. Just called in loops with a check for /// maximum difference. fn do_balancing<AccountId>( voter: &AccountId, budget: ExtendedBalance, elected_edges: &mut Vec<(AccountId, ExtendedBalance)>, support_map: &mut SupportMap<AccountId>, tolerance: ExtendedBalance ) -> ExtendedBalance where AccountId: Ord + Clone { // Nothing to do. This voter had nothing useful. // Defensive only. Assignment list should always be populated. 1 might happen for self vote. if elected_edges.is_empty() || elected_edges.len() == 1 { return 0; } let stake_used = elected_edges .iter() .fold(0 as ExtendedBalance, |s, e| s.saturating_add(e.1)); let backed_stakes_iter = elected_edges .iter() .filter_map(|e| support_map.get(&e.0)) .map(|e| e.total); let backing_backed_stake = elected_edges .iter() .filter(|e| e.1 > 0) .filter_map(|e| support_map.get(&e.0)) .map(|e| e.total) .collect::<Vec<ExtendedBalance>>(); let mut difference; if backing_backed_stake.len() > 0 { let max_stake = backing_backed_stake .iter() .max() .expect("vector with positive length will have a max; qed"); let min_stake = backed_stakes_iter .min() .expect("iterator with positive length will have a min; qed"); difference = max_stake.saturating_sub(min_stake); difference = difference.saturating_add(budget.saturating_sub(stake_used)); if difference < tolerance { return difference; } } else { difference = budget; } // Undo updates to support elected_edges.iter_mut().for_each(|e| { if let Some(support) = support_map.get_mut(&e.0) { support.total = support.total.saturating_sub(e.1); support.voters.retain(|i_support| i_support.0 != *voter); } e.1 = 0; }); elected_edges.sort_by_key(|e| if let Some(e) = support_map.get(&e.0) { e.total } else { Zero::zero() } ); let mut cumulative_stake: ExtendedBalance = 0; let mut last_index = elected_edges.len() - 1; let mut idx = 0usize; for e in &mut elected_edges[..] { if let Some(support) = support_map.get_mut(&e.0) { let stake = support.total; let stake_mul = stake.saturating_mul(idx as ExtendedBalance); let stake_sub = stake_mul.saturating_sub(cumulative_stake); if stake_sub > budget { last_index = idx.checked_sub(1).unwrap_or(0); break; } cumulative_stake = cumulative_stake.saturating_add(stake); } idx += 1; } let last_stake = elected_edges[last_index].1; let split_ways = last_index + 1; let excess = budget .saturating_add(cumulative_stake) .saturating_sub(last_stake.saturating_mul(split_ways as ExtendedBalance)); elected_edges.iter_mut().take(split_ways).for_each(|e| { if let Some(support) = support_map.get_mut(&e.0) { e.1 = (excess / split_ways as ExtendedBalance) .saturating_add(last_stake) .saturating_sub(support.total); support.total = support.total.saturating_add(e.1); support.voters.push((voter.clone(), e.1)); } }); difference }