# Universally liked candidate criterion

The universally liked candidate criterion or ULC is a voting criterion applicable to multi-winner methods that satisfy some proportionality criterion. The ULC is defined as follows:

After universally-liked candidates win, then there must be proportionality about the remaining winners.

A stronger version that doesn't require a separate definition of proportionality, also known as Independence of Universally Approved Candidates (IUAC) is:

Adding universally approved candidates and the right number of extra seats for them to fill should not make any difference to who gets elected to the other seats.

ULC is also known as "strong PR".[1]

## Example

Thiele fails the universally liked candidate criterion, and while that might not be the end of the world in itself, it’s closely related to a case where Thiele suffers an outright proportionality failure, described here and also in this paper. From the paper:

```20 to elect
2n voters: U1-U10, A1-A3
2n voters: U1-U10, B1-B3
n voters: C1-C6
```

The ideal result here would seem to be U1-U10, A1-A3, B1-B3 and C1-C4. The “UA” faction and the “UB” faction have 4/5 of the voters between them, and the “C” faction has 1/5. In terms of candidate numbers this result perfectly reflects that. However, Proportional Approval Voting would elect U1-U10, A1-A2, B1-B2 and C1-C6.

This is because after all the “U” candidates are elected, Proportional Approval Voting effectively considers UA and UB to be separate factions, meaning that they should each have twice the number of candidates as the C faction (12 to 6 in this case), rather than four times the total of the C faction when considered together. The fact that they are not completely separate factions is not taken into account.

If the UA faction and the UB faction were either in full agreement with each other or in complete disagreement, then they would get 16 candidates between them and the C faction would get 4 candidates. But this partial agreement counts against the UA and UB factions, and works in favour of the C faction, leaving the UA and UB factions with 14 candidates between them and the C faction with 6. While this isn’t a failure of PR in the simple way it has been defined in this paper, it would be a failure under a more nuanced definition.</poem>

## Criticism

```6 to elect
2 voters: U1, U2, U3, A1, A2, A3
1 voter: U1, U2, U3, B1
```

Under strong PR, the universally approved candidates (U1-3) should not affect the ratios of the other candidates elected. So the correct result would be U1-3, A1-2, B1 (or equivalent).

Thiele PAV elects U1-3, A1-3, failing the criterion. This result gives the A faction 6 candidates and the B faction 3 candidates, and [emphasis added] some may still argue that this is an acceptable proportional result.[2]