Better prime election. (#6939)

* Better prime election.

* improve docs

* more sensible variable names

* link to Borda count wiki

Co-authored-by: Shawn Tabrizi <shawntabrizi@gmail.com>

frame/elections-phragmen/src/lib.rs

@@ -87,7 +87,7 @@ use codec::{Encode, Decode};
 use sp_std::prelude::*;
 use sp_runtime::{
 	DispatchError, RuntimeDebug, Perbill,
-	traits::{Zero, StaticLookup, Convert},
+	traits::{Zero, StaticLookup, Convert, Saturating},
 };
 use frame_support::{
 	decl_storage, decl_event, ensure, decl_module, decl_error,
@@ -904,14 +904,20 @@ impl<T: Trait> Module<T> {
 			to_votes(Self::locked_stake_of(who))
 		};
 
-		let voters_and_votes = Voting::<T>::iter()
-			.map(|(voter, (stake, targets))| { (voter, to_votes(stake), targets) })
+		// used for prime election.
+		let voters_and_stakes = Voting::<T>::iter()
+			.map(|(voter, (stake, targets))| { (voter, stake, targets) })
+			.collect::<Vec<_>>();
+		// used for phragmen.
+		let voters_and_votes = voters_and_stakes.iter()
+			.cloned()
+			.map(|(voter, stake, targets)| { (voter, to_votes(stake), targets)} )
 			.collect::<Vec<_>>();
 		let maybe_phragmen_result = sp_npos_elections::seq_phragmen::<T::AccountId, Perbill>(
 			num_to_elect,
 			0,
 			candidates,
-			voters_and_votes.clone(),
+			voters_and_votes,
 		);
 
 		if let Some(ElectionResult { winners, assignments }) = maybe_phragmen_result {
@@ -965,17 +971,26 @@ impl<T: Trait> Module<T> {
 			// save the members, sorted based on account id.
 			new_members.sort_by(|i, j| i.0.cmp(&j.0));
 
-			let mut prime_votes: Vec<_> = new_members.iter().map(|c| (&c.0, VoteWeight::zero())).collect();
-			for (_, stake, targets) in voters_and_votes.into_iter() {
-				for (votes, who) in targets.iter()
+			// Now we select a prime member using a [Borda count](https://en.wikipedia.org/wiki/Borda_count).
+			// We weigh everyone's vote for that new member by a multiplier based on the order
+			// of the votes. i.e. the first person a voter votes for gets a 16x multiplier,
+			// the next person gets a 15x multiplier, an so on... (assuming `MAXIMUM_VOTE` = 16)
+			let mut prime_votes: Vec<_> = new_members.iter().map(|c| (&c.0, BalanceOf::<T>::zero())).collect();
+			for (_, stake, targets) in voters_and_stakes.into_iter() {
+				for (vote_multiplier, who) in targets.iter()
 					.enumerate()
-					.map(|(votes, who)| ((MAXIMUM_VOTE - votes) as u32, who))
+					.map(|(vote_position, who)| ((MAXIMUM_VOTE - vote_position) as u32, who))
 				{
 					if let Ok(i) = prime_votes.binary_search_by_key(&who, |k| k.0) {
-						prime_votes[i].1 += stake * votes as VoteWeight;
+						prime_votes[i].1 = prime_votes[i].1.saturating_add(
+							stake.saturating_mul(vote_multiplier.into())
+						);
 					}
 				}
 			}
+			// We then select the new member with the highest weighted stake. In the case of
+			// a tie, the last person in the list with the tied score is selected. This is
+			// the person with the "highest" account id based on the sort above.
 			let prime = prime_votes.into_iter().max_by_key(|x| x.1).map(|x| x.0.clone());
 
 			// new_members_ids is sorted by account id.