The Vote Seller's Dilemma

Despite common misconceptions, vote selling is already feasible with paper voting. For example, it is trivially easy to sign a blank vote-by-mail ballot and hand it over to a vote buyer. But this concern is magnified by internet voting because potential vote buyers can now more easily be located far away, outside law enforcement's jurisdiction, and automated.

In the context of public government elections, vote selling is already a serious crime and has been in the US criminal code for over 70 years (18 U.S.C. §597 (opens in a new tab)), carrying up to 2 years jail time and a $10k fine for a single willful instance, for both buyer & seller.

With that said, although vote selling is illegal, it is hard to detect without one of the two parties revealing the scheme, and therefore hard to enforce laws against it.

If we can make vote selling easier to detect, we can enforce accountability and deter it in the first place.

Proposed Approach

One key insight we can leverage is from Game Theory, specifically drawing from the two-party Prisoner's Dilemma:

The Prisoner's Dilemma illustrates how each player's individual interest — the “Nash equilibrium” — can be to always defect, no matter what action the other party takes.

Applicability to Vote Selling

Similarly, in the context of vote selling, the two parties involved — the vote buyer and the vote seller — face uncertainty regarding mutual trust. Consequently, both parties can be given a strong incentive to betray the other, disclosing the existence of the vote selling arrangement.

This proposal suggests leveraging the substantial criminal penalties to generate a powerful incentive for either party to betray the other. Alongside jail time, governments could impose a fine equal to 100 times the agreed-upon vote sale price.

Critically, a portion of the collected fine can be designated as a bounty reward for the party that exposes the vote-selling scheme. For instance, if the buyer and seller agree to a price of $50, a fine of $5,000 could be imposed, with a $250 reward offered to the defector who reports the illicit transaction, if it leads to successful prosecution.

Such a setup introduces enormous risk for potential vote buyers and sellers, effectively deterring their engagement in vote selling schemes.

To prevent false claims, individuals must provide verifiable proof and identify themselves, thereby risking perjury charges, while a jury is obligated to convict if the accused maintains their innocence.

Example Incentive Scheme:

Agreed Upon Price = $P
Punishment if Caught = Fined $P × 100 + Jail time
Reward for Reporting = $P × 5

In a situation akin to the Prisoner's Dilemma, it is consistently more advantageous for each party to betray the other. Given this understanding, both sides are aware that defection is also the preferable choice for their counterpart. Consequently, the ability of the two parties to trust each other is destroyed.

Voters who might have considered selling their votes now confront considerable risks of being ensnared in a trap, as the potential for deception and exposure is substantially heightened.

Even when the buyer is located outside the jurisdiction and may be more difficult to apprehend, the seller cannot be certain of this fact, as they could still be caught in a honeypot operation. Even in cases where the buyer can demonstrate their location outside the jurisdiction, they might still be motivated to collect the bounty reward instead. As a result, it is consistently more advantageous for the seller to betray the agreement rather than risk being betrayed themselves.

The SIV voting software can serve as a tool to inform voters about the legal ramifications of engaging in vote-selling schemes. By providing clear warnings and instructions on how to report any solicitations, the software can actively discourage participation in such activities and promote a more honest voting process.

In conclusion, a dual approach is proposed to combat vote selling. This involves establishing a robust legal framework that incentivizes both parties to betray one another, and implementing a voting interface that educates voters about the consequences, reporting rewards, and methods for taking action. By integrating these strategies, the likelihood of vote-selling attempts can be significantly reduced, resulting in greater trust in election outcomes.

Further Considerations

In the following sections, we delve into several additional implications and aspects of the proposal:

A Solution for Government Elections

The game-theoretic defense against vote buying is tailored specifically for government elections, relying on the criminal justice system to enforce rules and collect fines.

For non-government elections, establishing a Nash equilibrium that favors defection could potentially be achieved by requiring voters to submit a substantial financial deposit when voting. This deposit could then be confiscated if any instances of vote selling are detected.

Forensic and Remedial Capabilities of SIV

Secure Internet Voting (SIV) has robust forensic and remedial capabilities. In the event of corruption, whether due to vote selling or otherwise, individual votes can be corrected at any stage. Compromised votes can be invalidated, and the final results retallied, regardless of whether the issue is identified before or after tallying the election results. If necessary, affected voters can be issued new ballots to recast their votes.

Enhancing Security for Mail-In and In-Person Voting

As mentioned in the Vote Selling section, both mail-in and in-person voting systems are not entirely immune to vote selling attempts. For mail-in voting, votes can be easily transferred by signing a blank ballot and handing it over or sending it through the mail. While in-person voting presents a greater challenge, it is still possible for voters to prove their choices by recording a video of a marked ballot being dropped into a ballot box using a smartphone camera.

The proposed strategy, which incentivizes both parties to defect, has the potential to not only mitigate vote selling attacks on internet voting systems but also improve the security of mail-in and in-person voting methods.

SIV Creates More Evidence of Vote Selling

In the case of selling a mail-in ballot, it is plausible that the corruption may not leave any tangible evidence. The seller could hand over a blank signed ballot in exchange for cash from the buyer, and both parties could part ways without leaving any trace of the transaction.

Conversely, for SIV, if a voter attempts to sell their vote through a digital channel, there should be ample digital evidence available for either party to report the violation. Thus SIV — when combined with the proposed strong incentives for reporting — can achieve even greater resistance to vote selling than mail-in voting.

Self-Sustaining Enforcement Mechanism

An attractive feature of the proposed framework is its self-sustaining nature: the 5x reward is derived from the 100x fine imposed on the party caught violating the rules. The remaining 95x should be sufficient to fund enforcement efforts. As a result, this framework offers a cost-effective approach to combating vote selling.

Auto-Adaptive Enforcement

The proposed framework is responsive to the prevalence of vote selling. If vote selling is a rare occurrence, enforcement costs remain minimal. However, if vote buying becomes more common, it generates a financial incentive for individuals to set up honeypots to capture vote sellers. In essence, this system is a self-correcting mechanism that adapts to the current situation.

Investigating Deniability and Foreign Interference

The enforcement of voting security measures is partly influenced by the ambiguity faced by potential vote-sellers regarding the true nature of the buyer, which could potentially be a honeypot operation. For instance, a prospective seller might come across a website purporting to be based in a foreign jurisdiction and offering to purchase votes, only to discover that it is actually a local honeypot operation set up by their own neighbors. One extreme scenario could involve the potential buyer providing irrefutable evidence of their complete immunity from the voting jurisdiction, thus eliminating all deniability. This could occur if a voter was absolutely certain that they were communicating with a known adversary of the jurisdiction, such as the dictator of a rogue nation. However, several factors must be considered:

A rogue nation's leader might still choose to defect in order to collect a more significant bounty.
To achieve this, they would have to relinquish all possible deniability, a move inconsistent with existing global cyberattack strategies and likely to result in severe negative public relations.
Adopting such a practice would be akin to a declaration of war against the targeted country's sovereignty, constituting an extreme measure that would not be taken lightly and would be subject to its own forms of deterrence.

Examining Iterated Games

Individuals familiar with the Prisoner's Dilemma may identify a potential shortcoming in this approach when the problem is redefined as an Iterated Prisoner's Dilemma. Although both parties benefit more from defecting in any single round, successful cooperation for six consecutive rounds could yield more significant financial rewards than would be obtained by defecting in the first round. Nevertheless, several counterarguments can be presented to address this concern:

Neither party can confidently assert that they are in the clear following the first round. Their counterparty could be accumulating and collecting more evidence, with the possibility of defecting at any given moment.

The criminal statute of limitations may incorporate vulnerability to all past violations, allowing cumulative fines up to 100 times the original amount to overpower any acquired financial rewards. In other words, even if both parties appear to be cooperating, they are steadily accumulating increased liability and counterparty risk. Each counterparty's possible bounty rewards from exposing the scheme also continue to grow.

There is a practical question of whether defecting long after an election should still result in bounty payouts. We suggest a reduced bounty in this situation, such as twice the original amount rather than five times, as it is preferable to detect violations before an election is certified. However, it is still valuable to maintain long-term incentives for either party to defect.

Another factor to consider is that a counterparty may be cooperating in early rounds to establish a positive reputation, enabling them to attract a larger number of victims for later defection.

In summary, a counterparty's history of cooperation does not guarantee their continued cooperation in the future. Their incentive remains to feign cooperation initially and defect later when the potential payoff is greater. The possibility of a "long con" always exists.

Opportunity

The apprehension surrounding vote selling has posed a significant obstacle to the implementation of Secure Internet Voting for citizens. By implementing a comprehensive strategy, we can effectively deter vote selling endeavors through promoting continuous defection among both participating parties.