Published on April 1, 2025 12:53 PM GMT
A Karma system is a resource sharing mechanism based on an account of non-tradable rights. A recent paper named “Dynamic Recourse Allocation with Karma: An Experimental Study” (Elokda, Nax, Bolognani and Dörfler, 2024) describes this kind of mechanism. To summarize, agents have some rights to a given resource, and their need of the resource is variable (random) and private information. In a Karma system, each period agents bid for the resource using a token (named Karma) than can be stored in an individual Karma account. If an agent wins the auction she uses the resource, otherwise she increases her Karma account by an amount proportional to the Karma points spent by the auction winners (that can be used to bid for the resource in future rounds).
In this note there are two sections: in section 1 it is argued that as general rule Karma systems are dominated by simple monetary auctions, so every use case of a Karma system shall be grounded on a clear argument for the non-tradability of Karma by (general purpose) money. As the author of an early Karma system (“Storable votes-pay-as-you-win”, that is, Karma voting) I summarize that rationale for it.
In section 2, I first comment the experiment on Karma described in (Elokda, Nax, Bolognani and Dörfler, 2024), that I consider sound evidence for the good properties of Karma systems. On the other hand, I think that my own strategy (simulation of the outcomes arising from the optimal Nash strategy) and pure experimental economics are incomplete. To really understand mechanisms, we should mix artificial agents’ simulation and experiments. I am seeking a coauthor experienced in reinforcement learning to explore welfare properties of dynamic voting mechanisms using both artificial agents and human subjects.
Pivotability and Karma voting
The excellent literature review of the paper rightfully identifies the origin of Karma systems in the storable votes literature, and particularly identify my “Storable Votes-Pay with a pay-as-you-win mechanism” [ungated here] (Macías, 2024) as a Karma mechanism, that consequently can be named “Karma voting”:
“Trading votes across issues or proposals is an intuitively appealing and practically prevalent practice, yet it remains unclear to what extent vote trading improves welfare and how to design vote trading mechanisms optimally, as pointed out in Casella and Macè (2021) recent review. Casella and Macé (2021) distinguish between two types of vote trading: those in which votes are traded with other voters (Casella and Palfrey, 2019, 2021); and those in which votes are traded individually with one’s future self, referred to as storable (Casella, 2005) or qualitative votes (Hortala-Vallve, 2012)).
The latter type of storable votes, which yields particularly favorable efficiency gains in comparison to the other types of vote trading (Casella and Macé, 2021), is closely related to the aforementioned class of (finite-horizon) artificial currency mechanisms: voters are issued an initial budget of votes to cast in a (small) finite number of issues (Casella, 2005; Casella et al., 2006; Hortala-Vallve, 2012).
One recently proposed mechanism by Macías (2024) resembles Karma more closely: in this mechanism, votes are “paid” by the majority voters and subsequently redistributed, however, Macías (2024) studies a two voter only model. Our study thus complements the literature on storable votes, as we are motivated by resource allocations that are repeated more frequently and typically involve more players than in voting.”
I entirely embrace the proposed generalization, while in my view any use beyond voting shall include strong arguments on why “Karma tokens” shall be non-tradable. Money is a “universal Karma token”. The theorems of welfare economics, suggest that allowing the trading of Karma tokens, which in practice is equivalent to auctioning the resource, is optimal.
In the case of voting there are extremely good reasons to forbid auctioning. Suppose an election between two alternatives, where there are two types of players A and B, and for each player values the victory of its group as u>0 while the payoff of defeat us 0. If there are many voters, with no group coordinator, each voter values its vote as the product of the probability of casting the pivotal (decisive) vote multiplied by the difference between the preferred outcome and the other. That is:
Private valuation of a vote=Probability of casting the decisive vote [pivotability]*(Individual payoff of wining – Individual payoff of not wining).
Now, for a single voter in large electoral body, pivotability is astronomically low, so the private value of a vote is almost zero. If there is a small number of wealthy individuals with large stakes in the outcome of an election, they can easily buy these ultra-cheap votes. A simple way to express this idea is the following: for large electorates of rational non coordinated agents, vote auctioning (for money) is pivotability dominated; the outcomes valuation is almost irrelevant when compared to pivotability, so the vote auctioning mechanism does not collect the welfare relevant information (the outcomes valuation of the population), but mostly strategic assessments (self-assessed pivotability). Easily the “rich”, endowed with the possibility of buying votes, can be highly pivotal (in relative terms), and get their preferred outcomes no matter how numerous are the people who prefer each outcome, nor their preference intensity, because both are hidden under a veil of low pivotability.
This explains why Karma voting (based on non-tradable votes) is a good application of the Karma system. Similar arguments shall be provided for any Karma system to prove that specific Karma is not dominated by monetary auctioning (that is, universal Karma).
Experiments with human and artificial agents on Karma
Beyond the literature review and the presentation of the idea of a Karma system, Elokda, Nax, Bolognani and Dörfler (2024) is above all a paper on experimental results. The results of the paper go in the same direction than my own simulation for agents playing optimal Nash strategies computed by backward induction, and the metrics of social optimality are similar. Now, in my opinion both exploration techniques (Nash equilibrium exact computation and experiments) are simply too limited in the age of fast reinforcement learning.
A few months ago, I made this little note about the future of experimental economics:
An agentic turn to Experimental Economics
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4971482
“This article proposes a paradigm for integrating Experimental Economics with Agent-based models. Until now the primary focus of Experimental Economics has been to characterize aggregate discrepancies with respect to economic theory predictions or to characterize the impact of different setups (“treatments”) of a multi-agent game. On the other hand, given that aggregate discrepancies are caused by behavioral anomalies, the natural objective of experimental economics must be to calibrate artificial replicas of human subjects.
Given a multi-agent game, the following steps for the characterization of individual behavior are proposed: i) propose a “baseline” behavioral benchmark (by analytical means or reinforcement learning) for the considered multi-agent game, ii) conduct experiments with human subjects, iii) use the experimental results to fit behavioral models (capturing behavioral heterogeneity), iv) re-run the experiment with artificial agents and compare outcomes between the artificial and the human experiment.
When the outcomes of the human experiment closely match those of the experiment conducted with calibrated artificial agents the “human version” of the multi-agent game can be considered “solved”.”
That is why I am looking for a coauthor with experience in reinforcement learning to explore the welfare properties of different dynamic voting mechanisms, including my own, both for optimizing artificial agents and (perhaps) for human subjects. Please feel free to send this to anybody you consider could be interested in this project.
Discuss
