Asset voting

Asset voting is used to refer to a voting system in which votes are considered as "assets" given to candidates. If no candidate gets more than the winning threshold (i.e., a majority, in the single winner case), then the candidates can redistribute "their" votes to other candidates until a winner exists. Variations exist with different constraints on transfers - for example, the candidate with the fewest votes might be forced to redistribute their votes first. It is possible to force the negotiations to go on until there are enough candidates with quotas (say, Droop

Quotas) to fill all (or all but one of the) seats, which in the single-winner case would, under the former condition, mean requiring the winner to earn a majority of assets.

Asset voting was invented in 1874 by Lewis Caroll (Charles Dodgson), and independently reinvented and named by Forest Simmons and Warren Smith.

If used as a multi-winner voting method, it obeys most proportionality criteria, if the requisite assumptions about coalitions are extended to include candidates as well as voters. In such use, it is similar to delegable proxy systems except that, unlike such systems, it has public elections only at regularly scheduled intervals (proxies are not "revocable") and elects a fixed number of representatives with equal power.

Asset is Droop-proportional based on negotiator preferences (which can diverge from voter preferences), meaning that if a negotiator or group of negotiators hold a certain number of Droop Quotas of votes, they can guarantee the election of up to that number of their preferred candidates. Further, Asset always picks a winner or winner set that is in the Smith Set based on negotiators' preferences (which is not necessarily the same as the voters' preferences, since the negotiators may be corrupt, change preferences mid-negotiation, not know the voters' full preferences, etc.) if the negotiators are given enough time to negotiate and are honest with each other in their negotiating moves, meaning that if the negotiators have discussed every relevant permutation of winners or winner sets, Asset will always produce an outcome that can earn more votes during the negotiations than any other possible outcome, unless certain outcomes earn more votes than each other in a Condorcet cycle. In the single-winner case, if the negotiators are honest, strictly follow voter preferences, and have enough time to negotiate, then Asset becomes a Smith-efficient Condorcet method, and in the multiwinner case, resembles Condorcet PR methods such as CPO-STV and Schulze STV. The reasoning for this can in part be linked to the fact that Asset is an iterative voting method where the voters/negotiators are constantly updated on who is about to win if no change in votes occur, and they can therefore plan to defeat such candidates. Pairwise comparison is implicitly involved in this planning, as the negotiators must see if the candidates they prefer can obtain more votes from all negotiators than those who are about to win.

Asset can, under ideal conditions in the multiwinner case, render many if not all free-riding strategies needless; this is because, in some sense, the negotiators can do vote management themselves. Consider the example of three parties, A, B and C, where 51 voters vote for B candidates, 49 vote for A candidates, and 10 for C candidates, and there are 5 seats to be elected. Supposing every voter gives maximal support to all of the candidates of their chosen party, and no support for any other candidate, Party B will win 3 seats in most PR methods. However, if the 49 A voters divide themselves as evenly as possible between 3 of their candidates (17 of them bullet vote the first, 16 each bullet vote the second and third candidates), and a Droop quota is spent every time someone is elected in the PR method, then Party A will be able to win 3 seats instead. With Asset, the B candidates can agree to divide their 51 votes evenly between 3 of them (17 each), ensuring that their candidates will be 3 of the 5 candidates with the most votes when the negotiations end and thus win.

Sequential Asset Voting is a tweak to Asset that can be done several ways. One is by doing Asset sequentially in the multiwinner case: multiple rounds of negotiations are done, and after each round, the candidate(s) with the most votes are elected. If only one candidate is elected at a time, this can allow a majority to win every seat, and becomes Bloc Asset Voting, which is akin to deterministic Bloc methods such as Bloc Approval Voting. Bloc Asset Voting can also be done by doing regular Asset Voting but forbidding the negotiators from giving any candidate more than the negotiator's total starting votes divided by the number of seats (a negotiator with 20 votes could only give a given candidate a maximum of 4 votes if there are 5 seats to fill). It is also possible to spend or exhaust some votes after each seat is elected in Sequential Asset, which can influence the negotiation and potentially make Sequential Asset move in a continuum between majoritarianism and proportionality. If a Droop quota of votes is spent each time, for example, then Sequential Asset becomes at least semi-proportional based on negotiator preferences.

Asset Voting can be done algorithmically on ranked or rated ballots when certain assumptions are applied, such as the ones mentioned above. One main assumption is that every negotiator attempts to maximize their own satisfaction with the outcome. When there is a Condorcet cycle of negotiating outcomes in this algorithm that would give a voter incentive for Favorite Betrayal in most Condorcet methods, it is sometimes possible to prevent that if a cycle resolution method is applied and the algorithmic negotiators are then allowed to change their preferences for candidates in the cycle. As an example:

|2|A>B>C|

|3|C>A>B|

|4|C=B>A|

|2|A>B>C|

All 3 candidates are in a Condorcet cycle. Schulze picks C, so suppose that is the default outcome if no negotiation occurs. Based off of this, the algorithm can flip the 4 A>B>C voters to B>A>C to help resolve the cycle and elect B, because this change in expressed preference benefits these voters' actual preferences. Not enough C voters would have an incentive to negotiate to change the outcome again, so B is the Algorithmic Asset winner here (if Schulze is used for cycle resolution).