Is it possible to free ride in Asset?

Continuing the discussion from Different reweighting for RRV and the concept of Vote Unitarity:

In this example:

with this modification:

Droop Quota-spending PR methods would require Vote Management for Party B to maximize their guaranteed seat share.

But with Asset, it’s clearly possible to avoid that, since the candidates themselves can do the Vote Management for the voters. So in what scenarios is it necessary to do Vote Management in Asset to get a better result?

I’d guess that examples where Schulze STV or CPO-STV incentivize Hylland free-riding might be the ones best suited to show vulnerability to Hylland free riding in Asset as well, because Asset is, under certain conditions, Smith-efficient based on negotiator preferences, and those methods generally are Smith-efficient based on voter preferences.

So the example that I’ve (and probably others as well) used in the past to prove that all Hare-proportional ordinal PR methods and cardinal PR methods that pass Pareto are at least somewhat vulnerable to Hylland free riding and vote management is:
3 winners:
1 AD for cardinal, D>A for ordinal
1 BD/D>B
1 CD/D>C
By Pareto, D has to win a seat, and even if two factions (minus one voter for cardinal) remove their support for D, D still wins. This means that one of A, B, or C must lose. Assume without loss of generality that it is C. The C voters have an incentive to remove support for D, because if the entire faction does that, Hare proportionality requires that C be elected (without preventing the election of D, due to Pareto). Thus vote management has changed the outcome.

This form of example seems to be easily adapted to other forms of PR, although not party list cases, where the concept of factions does not exist (and where free-riding immunity is possible; as I’ve mentioned, the D’Hondt method is immune to Hylland free riding and vote management, although the tiebreaker can affect the mathematical certainty of this).

However, in Asset voting, this scenario may still be applicable. While the example seems unrealistic, at the party/faction level it seems plausible: D could be a popular party leader, and A, B, and C could be from different factions. If everyone gives their assets to D, D picks which factions win. However, a faction worried about not being chosen by D could give their assets directly to their faction’s candidate.

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