likwid/docs/reference/voting-methods.md

Voting Methods Reference

Detailed explanations of the voting methods available in Likwid.

Approval Voting

How It Works

• Voters select all options they approve of
• Each selection counts as one vote
• Options are ranked by total approvals

Best For

• Simple yes/no decisions
• Selecting multiple winners
• Low cognitive load

Example

Options: A, B, C, D
Voter 1 approves: A, B
Voter 2 approves: B, C
Voter 3 approves: A, C

Results:
A: 2 votes
B: 2 votes
C: 2 votes
D: 0 votes

Ranked Choice (Instant Runoff)

How It Works

1. Voters rank options from most to least preferred
2. If no option has majority, eliminate lowest
3. Redistribute eliminated votes to next preference
4. Repeat until winner has majority

Best For

• Single winner elections
• Reducing strategic voting
• Finding consensus candidate

Example

Round 1: A=40%, B=35%, C=25%
(C eliminated, votes transfer)
Round 2: A=45%, B=55%
Winner: B

Schulze Method

How It Works

1. Create pairwise comparison matrix
2. Find strongest paths between all pairs
3. Option X beats Y if strongest path X→Y > Y→X
4. Winner beats all others (Condorcet winner)

Best For

• Complex multi-option decisions
• When Condorcet winner exists
• Technical/policy decisions

Properties

• Condorcet consistent
• Clone independent
• Reversal symmetric

STAR Voting

How It Works

1. Voters rate each option 0-5 stars
2. Sum all ratings for each option
3. Top two scorers enter automatic runoff
4. In runoff, option preferred by more voters wins

Best For

• Balancing expressiveness and simplicity
• Reducing strategic voting
• When intensity of preference matters

Example

Scores: A=4.2 avg, B=3.8 avg, C=3.5 avg
Runoff: A vs B
Voters preferring A: 55%
Voters preferring B: 45%
Winner: A

Quadratic Voting

How It Works

• Each voter receives fixed voice credits (default: 100)
• Cost to cast N votes for an option = N²
• 1 vote = 1 credit, 2 votes = 4 credits, 3 votes = 9 credits
• Voters allocate credits across options

Best For

• Expressing intensity of preference
• Resource allocation decisions
• Preventing tyranny of majority

Example

100 credits available
Option A: 5 votes (25 credits)
Option B: 3 votes (9 credits)
Option C: 8 votes (64 credits)
Remaining: 2 credits

Strategic Considerations

• Spreading votes is efficient
• Strong preferences cost exponentially more
• Encourages honest preference revelation

Method Comparison

Method	Complexity	Expressiveness	Strategic Resistance
Approval	Low	Low	Medium
Ranked Choice	Medium	High	Medium
Schulze	High	High	High
STAR	Medium	High	High
Quadratic	Medium	Very High	High

Choosing a Method

For Simple Decisions

Use Approval - easy to understand, quick to vote.

For Elections

Use Ranked Choice or STAR - finds consensus, reduces spoiler effect.

For Technical Decisions

Use Schulze - handles complex preference structures.

For Budget/Resource Allocation

Use Quadratic - captures intensity of preference.