How Limited Preferential Voting Works
Papua New Guinea uses the Limited Preferential Voting (LPV) system for national elections. Under LPV, each voter marks three preferences on their ballot. This ensures the winner has broad community support, not just a narrow lead.
On the ballot paper, a voter writes the number 1 next to their first choice (most preferred candidate), 2 next to their second choice, and 3 next to their third choice.
To be a formal (valid) ballot, all three preferences must be filled in. A ballot missing any preference is considered informal and will not be counted.
The three preferences are limited — unlike full preferential systems used in some countries, PNG voters only rank three candidates, regardless of how many are contesting.
Step 1: Primary Count (1st Preferences)
All formal ballots are sorted by their 1st preference vote. Each candidate receives a pile of ballots where voters marked them as number 1. The total of all 1st preference votes across all candidates equals the total number of formal ballots cast.
Step 2: Check for Absolute Majority
The majority threshold is calculated: 50% + 1of the total formal votes. If any candidate's 1st preference count meets or exceeds this threshold, they are declared the winner immediately. No further counting is needed.
Step 3: Elimination of Lowest Candidate
If no candidate has a majority, the candidate with the fewest votes is eliminated from the count. Their ballots are set aside for redistribution. If two candidates are tied for the lowest, the one with the lower candidate number is eliminated first.
Step 4: Redistribution of 2nd Preferences
Each ballot from the eliminated candidate is examined. The 2nd preference marked on each ballot is checked. If that 2nd preference candidate is still active (not yet eliminated), the ballot is transferred to them. Their vote total increases by the number of ballots they receive.
After redistribution, the new totals for all remaining candidates are calculated. The total of all active candidates' votes plus any exhausted ballots still equals the total formal votes cast.
Step 5: Check Majority Again
After redistribution, the majority threshold is recalculated based on the remaining live (non-exhausted) votes. If any candidate now has enough votes to reach the new majority, they win. Otherwise, the process continues.
Step 6: Further Eliminations and 3rd Preferences
If still no majority, the next lowest candidate is eliminated. Their ballots are redistributed again. For ballots that were originally cast for this candidate, the 2nd preference is transferred. But for ballots that had already been transferred from a previously eliminated candidate, the 3rd preference is now checked instead (since the 2nd preference was the candidate just eliminated).
This means in later rounds, active candidates may receive votes from two sources:
- 2nd preference votes — from voters who listed the just-eliminated candidate as their 1st choice
- 3rd preference votes — from voters whose 1st choice was eliminated in a previous round, and whose 2nd choice is the candidate being eliminated now, so the ballot flows to their 3rd choice
Step 7: Repeat Until Winner
This cycle of eliminating the lowest, redistributing preferences, and checking for a majority continues until one candidate reaches the threshold. If only two candidates remain, the one with more votes wins.
Exhausted Votes
A ballot becomes exhaustedwhen all three of the voter's preferences have been eliminated. Since there are only three preferences in LPV, a ballot can exhaust after as few as two eliminations. Exhausted ballots are removed from the live count, which lowers the majority threshold. This means a candidate can win with fewer total votes than the original 50% + 1.
Vote Accounting
At every stage of the count, the following must balance: Active candidate votes + Exhausted ballots = Total formal votes. No votes are created or lost during redistribution — they are only transferred between candidates or marked as exhausted.
Imagine an election with 1,000 total formal votes and four candidates: A, B, C, and D.
Round 1: Primary Count
| Candidate | 1st Pref Votes | Status |
|---|---|---|
| A | 400 | Active (no majority — needed 501) |
| B | 300 | Active |
| C | 200 | Active |
| D | 100 | Eliminated (lowest) |
| Total | 1,000 | = 1,000 formal votes |
No candidate has 501 votes. D is eliminated. D's 100 ballots are examined for their 2nd preferences.
Round 2: Redistribution of D's Votes
Of D's 100 ballots: 40 listed B as 2nd preference, 50 listed C as 2nd preference, and 10 listed A as 2nd preference.
| Candidate | Prev. Votes | + Transferred | New Total | Status |
|---|---|---|---|---|
| A | 400 | +10 (2nd pref from D) | 410 | Active |
| B | 300 | +40 (2nd pref from D) | 340 | Active |
| C | 200 | +50 (2nd pref from D) | 250 | Eliminated (lowest) |
| Exhausted | 0 | 0 | 0 | |
| Total | 1,000 | = 1,000 formal votes |
Still no majority (need 501). C is eliminated. C's 250 ballots must be redistributed.
Round 3: Redistribution of C's Votes (2nd and 3rd Preferences)
C has 250 ballots. Some are original (voters who picked C as 1st choice), and 50 came from D in the previous round.
- C's original 200 ballots: Their 2nd preference is checked. Say 120 listed A and 70 listed B, and 10 listed D (already eliminated, so those exhaust).
- 50 ballots transferred from D: These ballots had D as 1st choice and C as 2nd choice. Now C is eliminated too, so the 3rd preference is checked. Say 30 listed A and 15 listed B, and 5 had no valid 3rd preference (exhaust).
| Candidate | Prev. Votes | + Transferred | New Total | Status |
|---|---|---|---|---|
| A | 410 | +150 120 as 2nd pref from C 30 as 3rd pref from D voters via C | 560 | Winner (needed 493) |
| B | 340 | +85 70 as 2nd pref from C 15 as 3rd pref from D voters via C | 425 | Runner-up |
| Exhausted | 0 | +15 | 15 | 10 had D as 2nd (eliminated), 5 had no valid 3rd |
| Total | 1,000 | = 1,000 formal votes |
A reaches 560 votes, exceeding the new majority threshold of 493 (50% + 1 of 985 live votes). Candidate A wins.
Key Takeaways
- 1st preference votes determine the initial standing, but 2nd and 3rd preferences decide the winner when no one has a majority.
- 2nd preference votes transfer directly from the just-eliminated candidate to active candidates.
- 3rd preferencevotes come into play when a ballot's 1st choice was eliminated in a previous round and their 2nd choice is now also eliminated — the ballot flows to the 3rd choice.
- At every stage: active votes + exhausted = total formal votes. No votes are created or lost.
- Exhausted ballots lower the majority threshold, so a winner can emerge with fewer votes than the original 50% + 1.