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; generally speaking, a Droop or Hare Quota), 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.

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 allows a negotiator or group of negotiators who hold a certain number of Droop Quotas of votes to 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 which case one of those cycling outcomes will win. 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 (these transformations can be observed by turning Asset Voting into an algorithm using various assumptions, as mentioned below). The reasoning for this can in part be linked to the fact that Asset is an iterative voting method (it is almost like an iterative version of FPTP; iterative voting methods are generally more Condorcet efficient than their non-iterative equivalents) where the voters/negotiators are constantly updated on who is about to win if no change in votes occur (i.e. which set of candidates of a size equal to the number of seats to be filled have more votes committed to them so far), 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 over those about to win 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.

Asset Voting can be done algorithmically on ranked or rated ballots when certain assumptions are applied, such as the ones mentioned above (here is a visualization of the algorithm). 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 in Algorithmic Asset if a cycle resolution method is applied and the algorithmic negotiators are then allowed to optimize their preferences for candidates in the cycle in response to the cycle resolution method's chosen winner. 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 that would be 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 (since B would then be the only member of the Smith Set, B can't be overtaken by anyone else), because this change in expressed preference benefits these voters' actual preferences. Then, not enough C voters would have an incentive to negotiate to elect someone other than B. It may be possible for some cycles to only be resolvable when certain cycle resolution methods are used as default methods in Algorithmic Asset and not others.

Asset Voting also has sequential and Bloc versions of itself, which are generally less proportional and more majoritarian than regular Asset in the multiwinner cases. Both can be algorithmized as well.