Crate tp_npos_elections

A set of election algorithms to be used with a tetcore 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.
• phragmms(): Implements a hybrid approach inspired by Phragmén which is executed faster but it can achieve a constant factor approximation of the maximin problem, similar to that of the MMS algorithm.
• balance: Implements the star balancing algorithm. This iterative process can push a solution toward being more balances, which in turn can increase its score.

Terminology

This crate uses context-independent words, not to be confused with staking. This is because the election algorithms of this crate, while designed for staking, can be used in other contexts as well.

Voter: The entity casting some votes to a number of Targets. This is the same as Nominator in the context of staking. Target: The entities eligible to be voted upon. This is the same as Validator in the context of staking. Edge: A mapping from a Voter to a Target.

The goal of an election algorithm is to provide an ElectionResult. A data composed of:

• winners: A flat list of identifiers belonging to those who have won the election, usually ordered in some meaningful way. They are zipped with their total backing stake.
• assignment: A mapping from each voter to their winner-only targets, zipped with a ration denoting the amount of support given to that particular target.

// the winners.
let winners = vec![(1, 100), (2, 50)];
let assignments = vec![
    // A voter, giving equal backing to both 1 and 2.
    Assignment {
		who: 10,
		distribution: vec![(1, Perbill::from_percent(50)), (2, Perbill::from_percent(50))],
	},
    // A voter, Only backing 1.
    Assignment { who: 20, distribution: vec![(1, Perbill::from_percent(100))] },
];

// the combination of the two makes the election result.
let election_result = ElectionResult { winners, assignments };

The Assignment field of the election result is voter-major, i.e. it is from the perspective of the voter. The struct that represents the opposite is called a Support. This struct is usually accessed in a map-like manner, i.e. keyed by voters, therefor it is stored as a mapping called SupportMap.

Moreover, the support is built from absolute backing values, not ratios like the example above. A struct similar to Assignment that has stake value instead of ratios is called an StakedAssignment.

More information can be found at: https://arxiv.org/abs/2004.12990

Macros

generate_solution_type

Generates a struct to store the election result in a small way. This can encode a structure which is the equivalent of a tp_npos_elections::Assignment<_>.

Structs

Assignment	A voter’s stake assignment among a set of targets, represented as ratios.
Candidate	A candidate entity for the election.
Edge	A vote being casted by a Voter to a Candidate is an Edge.
ElectionResult	Final result of the election.
StakedAssignment	A voter’s stake assignment among a set of targets, represented as absolute values in the scale of ExtendedBalance.
Support	A structure to demonstrate the election result from the perspective of the candidate, i.e. how much support each candidate is receiving.
Voter	A voter entity.

Enums

Error

The errors that might occur in the this crate and compact.

Traits

CompactSolution	A common interface for all compact solutions.
EvaluateSupport	Extension trait for evaluating a support map or vector.
FlattenSupportMap	Helper trait to convert from a support map to a flat support vector.
IdentifierT	an aggregator trait for a generic type of a voter/target identifier. This usually maps to tetcore’s account id.
PerThing128	Aggregator trait for a PerThing that can be multiplied by u128 (ExtendedBalance).
TupleRef	A common wrapper trait for both (&A, &B) and &(A, B).

Functions

assignment_ratio_to_staked	Converts a vector of ratio assignments into ones with absolute budget value.
assignment_ratio_to_staked_normalized	Same as assignment_ratio_to_staked and try and do normalization.
assignment_staked_to_ratio	Converts a vector of staked assignments into ones with ratio values.
assignment_staked_to_ratio_normalized	Same as assignment_staked_to_ratio and try and do normalization.
balance	Balance the weight distribution of a given voters at most iterations times, or up until the point where the biggest difference created per iteration of all stakes is tolerance. If this is called with tolerance = 0, then exactly iterations rounds will be executed, except if no change has been made (difference = 0).
is_score_better	Compares two sets of election scores based on desirability and returns true if this is better than that.
phragmms	Execute the phragmms method.
reduce	Reduce the given Vec<StakedAssignment<IdentifierT>>. This removes redundant edges from without changing the overall backing of any of the elected candidates.
seq_phragmen	Execute sequential phragmen with potentially some rounds of balancing. The return type is list of winners and a weight distribution vector of all voters who contribute to the winners.
seq_phragmen_core	Core implementation of seq-phragmen.
to_support_map	Build the support map from the winners and assignments.
to_supports	Same as to_support_map except it calls FlattenSupportMap on top of the result to return a flat vector.
to_without_backing	consumes a vector of winners with backing stake to just winners.

Type Definitions

CandidatePtr	A pointer to a candidate struct with interior mutability.
ElectionScore	The score of an assignment. This can be computed from the support map via EvaluateSupport::evaluate.
ExtendedBalance	A type in which performing operations on vote weights are safe.
SupportMap	Linkage from a winner to their Support.
Supports	A target-major representation of the the election outcome.
VoteWeight	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.
WithApprovalOf	A winner, with their respective approval stake.