📈 economics

On voting rules satisfying false-name-proofness and participation

This paper investigates voting rules in settings with unverified identities, demonstrating that while false-name-proofness and participation are generally incompatible with neutrality and onto properties in broad preference domains, they can be simultaneously satisfied alongside anonymity, object neutrality, and tops-only properties specifically within the maximal domain of separable preferences.

Original authors: Agustin G. Bonifacio, Federico Fioravanti

Published 2026-05-15

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Agustin G. Bonifacio, Federico Fioravanti

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are organizing a massive online vote to decide on a new park feature. You have a list of options: a fountain, a playground, a garden, or maybe all of them combined. In a perfect world, everyone shows up with one ID, votes once, and the result is fair. But in the messy reality of the internet, things get tricky.

This paper is like a detective story investigating the rules of the game to see if we can design a voting system that is unhackable by two specific tricks:

The "Sock Puppet" Trick (False-Name-Proofness): A voter creates fake accounts to cast the same vote multiple times.
The "Walkout" Trick (Participation): A voter decides, "If I don't vote, the result will be better for me," so they stay home to manipulate the outcome.

The authors ask: Can we write a set of rules that stops both of these tricks while also being fair to everyone and everything?

Here is what they discovered, broken down into simple concepts.

1. The "Identity Crisis" (Universal Domain)

First, the authors looked at a scenario where the options are completely random and unstructured (like choosing between "Apples," "Blue," and "Tuesday").

They found a surprising twist: If you build a rule that stops people from using fake names and stops people from benefiting by walking out, that rule automatically becomes "Anonymous."

The Analogy: Imagine a voting booth where the machine doesn't care who you are, only what you voted for. The authors proved that if your system is immune to sock puppets and walkouts, it must treat every voter as a faceless number. You cannot give special weight to "Voter A" vs. "Voter B."

The Bad News: Because the system must treat everyone equally (Anonymous), it cannot treat the options equally (Neutral).

The Metaphor: Imagine a judge who must treat every defendant exactly the same. If the judge does that, they can't also promise to treat every crime exactly the same. The math shows you can't have a system that is perfectly fair to both the voters and the options if the options are totally unstructured.

2. The "Shopping Cart" Problem (Subsets of Objects)

Next, they looked at a more realistic scenario: The options are combinations of things. Think of a shopping cart. You can buy just an apple, just a banana, or both. This is the "Domain of Subsets."

Here, they added three more "nice-to-have" rules for a good voting system:

Ontoness: Every possible combination (even "nothing" or "everything") should be a possible winner.
Tops-Only: The system should only need to know your #1 favorite choice, not your whole ranking of 100 items. (This is crucial for online voting where people get tired).
Object Neutrality: The names of the items shouldn't matter. If you swap "Apples" and "Bananas" in everyone's list, the result should just swap accordingly.

The Big Impossibility:
When you try to combine all five of these good qualities (stopping sock puppets, stopping walkouts, plus the three "nice-to-haves") in a world where people can have any crazy preference, it is impossible.

The Analogy: It's like trying to build a car that is:
1. Bulletproof.
2. Waterproof.
3. Fireproof.
4. Drives itself.
5. Costs $500.
  The paper proves that for "any possible preference," you cannot build this car. If you try to satisfy all these conditions, the math breaks down.

3. The "Magic Zone" (Separable Preferences)

So, is the game over? Not quite. The authors found a special "Magic Zone" where all these rules do work.

This zone is called Separable Preferences.

The Metaphor: Imagine you are packing a suitcase.
- Separable: You love your toothbrush (it's "good") and you hate your old socks (they are "bad"). If you have a toothbrush, adding another toothbrush makes the suitcase better. If you have socks, adding more socks makes it worse. Your choices are consistent.
- Non-Separable (The Chaos): You love the toothbrush unless you also have the socks, in which case you hate the toothbrush. Or maybe you only want the socks if you also have a hat. Your preferences depend on weird combinations.

The paper shows that if you restrict the voters to only have "Separable" preferences (where items are consistently good or bad on their own), you can build a perfect voting system that satisfies all five rules.

4. The "Edge of the Cliff" (Maximality)

Finally, the authors asked: "How big can this Magic Zone be? Can we let in a few voters with 'weird' (non-separable) preferences?"

The Answer: No. The Magic Zone is already at its maximum size.

The Analogy: Imagine the "Separable" preferences are a solid island. The "Non-separable" preferences are the ocean. The paper proves that the island is already as big as it can possibly be. If you try to add even one single person with a weird, non-separable preference to the island, the perfect voting system collapses. The "water" (the impossibility) will flood in, and at least one of your five rules will break.

Summary

The Problem: In online voting, people can cheat by using fake names or by refusing to vote.
The Discovery: If you build a system to stop these cheats, you lose the ability to treat voters differently, which makes it impossible to treat all options fairly in a general setting.
The Solution: If the choices are combinations of items (like a shopping cart), you can have a perfect system, BUT only if everyone's preferences are "consistent" (Separable).
The Limit: You cannot expand this solution to include people with "inconsistent" or "weird" preferences. The moment you do, the perfect system breaks.

The paper essentially draws a hard line in the sand: For a voting system to be truly robust against these specific internet-era cheats, it must rely on voters having consistent, predictable preferences.

Technical Summary: On Voting Rules Satisfying False-Name-Proofness and Participation

1. Problem Statement

The paper investigates the existence and properties of voting rules in environments where voter identities are difficult to verify, such as online settings. In such contexts, voters face two primary strategic manipulation opportunities:

False-name manipulation: A voter casts multiple votes under different identities to influence the outcome.
Abstention manipulation (No-show paradox): A voter benefits by abstaining from voting rather than participating.

The authors analyze voting rules that are immune to these manipulations, defined respectively as false-name-proofness and participation. The study examines these properties across two distinct domains of social alternatives:

The Universal Domain: Alternatives are unstructured, and all strict linear orders over them are admissible.
The Domain of Subsets of Objects: Alternatives are subsets of a given set of objects $O$ (i.e., $A = 2^O$ ). This domain allows for the consideration of specific preference structures, such as separable preferences, where the value of an object is independent of the set it is added to.

2. Methodology and Axioms

The authors employ an axiomatic approach, defining a voting rule as a mapping from preference profiles to alternatives. They evaluate rules based on the following desirable properties:

False-name-proofness: A voter cannot benefit by submitting additional votes identical to their original preference (a weaker condition than strong false-name-proofness, which allows submitting different preferences).
Participation: A voter never obtains a worse outcome by voting than by abstaining.
Anonymity: The rule treats all voters symmetrically; permuting voter identities does not change the outcome.
Neutrality (and Object Neutrality): The rule treats all alternatives symmetrically. In the subset domain, this is relaxed to object neutrality, where permuting the names of the underlying objects does not affect the chosen subset.
Ontoness: Every possible alternative (or subset) can be the outcome for some profile.
Tops-onliness: The outcome depends solely on the top choice of each voter.

The analysis proceeds by establishing logical relationships between these axioms and proving impossibility theorems for specific combinations of properties on specific domains.

3. Key Contributions and Results

A. The Universal Domain

The authors first analyze the universal domain of preferences.

Implication of Anonymity: The paper proves that any voting rule satisfying both false-name-proofness and participation must be anonymous (Proposition 2). This is derived by showing that if a voter's identity changes but their preference remains the same, the outcome is invariant (Lemma 1).
Incompatibility with Neutrality: Since anonymity and neutrality are generally incompatible on the universal domain for three or more alternatives, the authors conclude that no voting rule on the universal domain can simultaneously satisfy false-name-proofness, participation, and neutrality (Proposition 3). This result extends previous impossibility findings (e.g., Conitzer, 2008) to the weaker notion of false-name-proofness.

B. The Domain of Subsets of Objects

The authors then shift to the domain where alternatives are subsets of objects, relaxing neutrality to object neutrality. They investigate whether the five properties (ontoness, tops-onliness, false-name-proofness, participation, and object neutrality) can coexist.

General Impossibility: The paper establishes that no voting rule satisfies all five properties simultaneously on the domain of all preferences over subsets of objects (Theorem 1). The proof demonstrates that ontoness and tops-onliness, combined with false-name-proofness and participation, force the rule to behave in a way that contradicts object neutrality when analyzing reduced societies (e.g., one or two voters).
Independence of Axioms: The authors show that the impossibility is non-trivial because the five axioms are logically independent. They provide examples of rules that satisfy any four of the five properties but fail the fifth.

C. Maximality of Separable Preferences

The paper revisits the domain of separable preferences, where Fioravanti and Massó (2024) had previously characterized rules satisfying these properties (specifically, voting by quota rules). The authors address whether this domain can be enlarged while maintaining the compatibility of all five properties.

Maximality Result: The paper proves that the domain of separable preferences is maximal for the set of rules satisfying ontoness, tops-onliness, false-name-proofness, participation, and object neutrality (Theorem 2).
Mechanism of Failure: The proof demonstrates that for any non-separable preference added to the domain, there exists at least one rule (specifically, extensions of majority-like quota rules) that satisfies all properties on the separable domain but violates participation when extended to include the non-separable preference. This implies that separability is a necessary condition for the compatibility of these axioms across the entire class of such rules.

4. Significance and Claims

The paper claims to provide a rigorous characterization of the limits of manipulation-proof voting in anonymous environments. Its significance lies in three main areas:

Clarifying the Cost of Immunity: It establishes that preventing both duplicate voting and beneficial abstention fundamentally requires anonymity, which in turn precludes neutrality in unstructured settings.
Robustness of Separable Preferences: It demonstrates that the positive results found in the literature for separable preferences are not merely artifacts of that specific domain but represent a structural boundary. The domain of separable preferences is the largest possible domain where a class of rules can satisfy all five desirable properties simultaneously.
Practical Implications for Online Voting: The findings suggest that platforms designing voting mechanisms for environments with unverified identities (e.g., blockchain governance or online polls) face a trade-off. To achieve ontoness, tops-onliness, and object neutrality alongside immunity to false-name and no-show manipulations, the system must either restrict the admissible preferences to separable ones or accept that some natural rules will fail when preferences exhibit complementarities or substitution effects.

The authors conclude that the separable domain serves as a well-defined benchmark where all desiderata can be jointly satisfied, and any relaxation of this domain inevitably leads to the violation of at least one property for some rules within the characterized class.