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.