Free riding

Free riding is a form of tactical voting which affects proportional multi-winner systems. The basic strategy is to not vote for all of the candidates you support, since you expect others to elect them. This is a particularly useful strategy when those who elect them for you do not support those you do vote for. The existence of this strategy is a byproduct of mechanisms used to increase proportional representation.

Woodall free riding
Woodall free riding is a strategy in STV elections in which a voter ranks a candidate whom the voter expects will be eliminated, so that their vote is not spent on a candidate who exceeds the quota on the first count. Not all proportional representation methods are vulnerable to Woodall free riding, for example, Meek STV isn't, and most cardinal methods are also immune.

Hylland free riding
Hylland free riding is when a voter buries candidates who are certain to be elected, in order to prevent their ballot from being spent electing them. In ordinal methods, this often takes the form of ranking candidates whose election is uncertain above the stronger candidates, and in cardinal methods this would take the form of giving points only to candidates whose election is uncertain. All Droop proportional ordinal methods and all cardinal methods with proportional party-list cases that pass the Pareto criterion are vulnerable to Hylland free riding.

Incompatibility
Invulnerability to Hylland free riding is incompatible with the Droop proportionality criterion. More broadly, if a method gives a seat to every candidate that's ranked first by more than a Droop quota, that method is vulnerable to Hylland free riding. The following two-seat election shows how:

10: A>B>C 35: A>C>B 25: B>C>A 30: C>B>A

The Droop quota is $33 1/3$. By Droop proportionality, A gets the first seat. The second seat must go to either B or C. Suppose B gets the second seat. Then the voters who prefer C to B can bury A:

10: A>B>C 24: A>C>B 11: C>A>B 25: B>C>A 30: C>B>A

and now Droop proportionality requires that both A and C are elected. On the other hand, if C gets the second seat, then the voters who prefer B to C can bury A:

10: B>A>C 35: A>C>B 25: B>C>A 30: C>B>A

and Droop proportionality requires that both A and B are elected.

Vote management
Vote management is when multiple people collectively decide how to vote to optimize the ability to free ride. It takes advantage of Hylland free riding.

Example: Suppose 50 voters pick Party A, 11 voters pick B, and 10 voters pick each party from C to Z. Most quota-based (largest remainder method-based) methods would pick (A, C). Now, suppose the 50 A voters instead split into two groups of 25 for Party A1 and Party A2; most quota-based methods pick (A1, A2). So by evenly dividing their votes, Party A voters elect more of their preferred candidates. Note that one implication of this is that voters may not be able to choose who to vote for, since they may have to follow party leadership orders on which candidates to orchestrate the division of votes for.

Immune systems
Many systems are not susceptible to free riding. All Single Member District systems, such as Single Member Plurality are immune to Free Riding. Similarly so are Bloc voting. This is because these systems have no mechanism designed to improve Proportional Representation.

Weighted systems
Some multi-member methods give each winner a weighted vote in the assembly. These methods are generally immune to free riding for the purpose of increasing a winner's voting weight, because voting for a winner will always help him by increasing his weight. However, the methods can still be susceptible to free riding when deciding who the winners will be: in some cases, a voter may help deny opposition candidates a seat by using vote management.

Multi-Member Systems
Systems with Hare quotas have greater incentive to Hylland free ride / manage votes than ones with Droop quotas. Single transferable vote elections nearly always use Droop quotas, but the fact that the votes are transferable takes the risk out of free riding. However, in Multi-Member Score voting systems like Reweighted score voting, it is riskier to free ride than ranking because they do not transfer votes but reweight. In fact, Woodall free riding doesn't really exist in most score-based methods. So there are two factors pushing in opposite directions. Multi-Member Score voting with Droop quotas would be better than STV, but that might also harm the system in honest cases. Most STV rules (i.e. not Meek) are also susceptible to Woodall free riding, though that is not useful for vote management. Condorcet PR methods such as CPO-STV and Schulze STV resist vote management better than standard STV.

Cardinal PR methods that use the Sequentially Shrinking Quota modification can limit cases of free-riding.

Party-list proportional representation
Namibia and Hong Kong both use the largest remainder method of pick-one party list proportional representation without a threshold. Thresholds make vote management much harder and much less effective, so while it might sometimes be mathematically possible, in practice it doesn't happen. Namibia is a one-party dominated state. The National Assembly elections that use the method elect all 96 seats in one nationwide electoral district. Last time, the largest party got 80% of the vote. Vote management is not practiced, and it wouldn't matter.

In Hong Kong, there are multi member districts with 5, 6, or 9 seats. Vote management is very common. There are several pro-democracy and pro-Beijing parties, and parties often run multiple lists in a district, and divide their voters geographically. No single list has won multiple seats in the past two cycles. In effect, it is SNTV. These elections are more competitive than in Namibia, although their influence on policy is limited by Beijing's use of “functional constituencies” to ensure that their preferred candidates control the legislative council.

In practice, vote management in score methods with list cases of largest remainder would likely involve bullet voting for individuals and so look similar to vote management in Hong Kong. Vote management would be more essential in Monroe and allocation than SSS, because voters giving midrange scores to candidates are less likely to contribute to the quota in those systems; the candidate's strongest supporters pay as much as possible first. This means that a party that doesn't do any vote management will probably pay full quotas for their first seats, since a party nominee's strongest supporters are likely to be partisans. In contrast, with SSS, midrange supporters for a candidate pay some of the cost, so the base of the winning candidate's party will not pay the entire Hare quota even without vote management.