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Social Choice Around the Block: On the Computational Social Choice of Blockchain

One of the most innovative aspects of blockchain technology consists in the introduction of an incentive layer to regulate the behavior of distributed protocols. The designer of a blockchain system faces therefore issues that are akin to those relevant for the design of economic mechanisms, and faces them in a computational setting. From this perspective the present paper argues for the importance of computational social choice in blockchain research. It identifies a few challenges at the interface of the two fields that illustrate the strong potential for cross-fertilization between them.

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1. Introduction

A blockchain is a decentralized state machine, in its simplest form, a decentralized ledger for financial transactions. The machine is controlled by several distinct processes, called nodes or agents, and computes by packaging state transitions (e.g., the order of transfering tokens from Alice’s account to Bob’s) in batches, which are called blocks. Each block determines the next global state of the machine (e.g., the next state of the ledger, where Alice’s account has tokens less and Bob’s more). Each new block is appended to the list of older blocks, thereby determining a growing append-only list of global states of the machine—its computation history. Crucially, each block points in a temper-proof way (via a cryptographic hash) to the previous block to which it was appended, thereby enforcing an immutable description of the history of the machine. The core of a blockchain is the protocol that the nodes follow in order to agree on which transitions to incorporate into the list, i.e., to achieve consensus on the state of the machine.

Paper motivation

Blockchain was born as the backbone of the Bitcoin cryptocurrency. The consensus protocol behind Bitcoin, known as Nakamoto consensus Nakamoto (2008); Garay et al. (2015), showed that such a decentralized consensus on an append-only list is possible even in large, open peer-to-peer networks. This was a significant breakthrough with respect to existing approaches to consensus, which worked specifically on systems of limited size with controlled access. This breakthrough relied on one key insight: nodes in an open system cannot be controlled, so their influence on consensus should be kept at bay by linking it to the ownership of a non-monopolizable resource—in the case of Bitcoin, computing power. In other words, nodes in an open network cannot be controlled nor trusted, but can be incentivized. Nodes that contribute to achieving consensus are rewarded with (they ‘mine’) tokens, that is, units of currency. This is the key intuition behind the application to consensus of the Proof-of-Work (PoW) technique (originally developed to thwart email spamming Dwork and Naor (1992)), which has proven extremely robust, maintaining the Bitcoin blockchain for over a decade (cf. for recent overviews Narayanan et al. (2016); Wattenhofer (2017)). So, blockchain consensus is the result of a rational response to incentives.

Traditionally, research in blockchain has focused mostly on the cryptographic foundations and the distributed computing aspects (e.g., protocol correctness) of the technology. At the same time, a game-theoretic perspective on blockchain protocols has also been gaining attention: is behavior in accordance with the protocol economically rational, in some precise equilibrium-theoretic sense? In other words, are protocols strategy-proof? This game-theoretic perspective has historically been marginal in distributed computing Abraham et al. (2011), but has proven significant in blockchain. By now, it has been extensively applied—including by researchers in the AAMAS community—to Nakamoto consensus (e.g., Eyal (2015); Sapirstein et al. (2016); Sompolinsky and Zohar (2018); Alkalay-Houlian and Shah (2019)), as well as to other protocols (e.g., Abraham et al. (2016); Kiayias et al. (2017); Amoussou-Guenou et al. (2020); Chen et al. (2021)). See Judmayer et al. (2021) for an extensive recent overview. However, the economic issues that the designer of a blockchain system faces go well beyond incentive-compatibility alone, and reflect broad issues in the design of collective decision-making mechanisms, such as forms of equity and fairness. This interface with the economic theory of group decision-making, and specifically social choice theory, is the focus of the present paper.

Paper contribution

The contribution of this paper consists in arguing how social choice theory, and its algorithmically-focused branch—computational social choice—have an important role to play in providing stronger foundations for the principled development of blockchain technology. This paper sketches a number of research challenges at the interface of computational social choice and blockchain. I claim there exists now a perfect match between the state-of-the-art in blockchain research on the one hand, and the state-of-the-art in on computational social choice on the other. Blockchain offers a wealth of novel questions that can push the boundaries of the existing body of results of computational social choice, and in doing so contribute concrete solutions to the challenges blockchain research itself currently faces.

To substantiate this claim, this paper reviews how key mechanisms that have a long tradition within (computational) social choice find deployment in blockchain systems: randomized mechanisms, voting mechanisms, and trust mechanisms. In reviewing these mechanisms this paper identifies challenges that their deployment in blockchain gives rise to, phrasing them in terms of properties that, again, have occupied social choice theorists in the past: fairness of lotteries, manipulation of voting, and false-name proofness of trust mechanisms. Such an overview has no claim to be exhaustive and rather aims at illustrating, by means of examples, the potential for cross-fertilization between the two research areas. Given the nature of this paper I will try to limit technical jargon to a minimum, use informal language as much as possible and just convey the gist of my arguments without resorting to explicit mathematical details.

2. Randomization

2.1. Lotteries in Blockchain and Social Choice

Randomization has a long tradition in distributed computing as a way to bypass impossibility results such as the so-called FLP impossibility theorem Fischer et al. (1985).111The Fisher, Lynch, Paterson (FLP) impossibility result states that in an asynchronous system no deterministic consensus protocol exists which can tolerate even just one faulty node, where a faulty node is a node which stops interacting with the protocol. Blockchain has further stressed the importance of randomization. Lotteries are at the heart of the main approaches to blockchain consensus such as proof-of-work (PoW, currently used in both Bitcoin and Ethereum Buterin (2013)) and proof-of-stake (PoS, currently used for instance in the Ouroboros protocols Daian et al. (2016); David et al. (2017) and Algorand Gilad et al. (2017)). At a high level, and leaving network latency issues aside, these protocols work as follows: nodes participate in a distributed lottery; the winner appends a new block to the chain (or, depending on the specific protocol, becomes part of a committee which will then vote on the block to be appended) and receives a compensation in the native currency—what is referred to as mining. Importantly, the chances of winning this lottery depend on a resource that is assumed not to be monopolizable—such as computational power (in PoW) or currency ownership (in PoS). This makes participation to the lottery (directly or indirectly) costly and prevents the manipulation of the lottery through identity forging (the so-called Sybil attack Douceur (2002)). Based on this blueprint, several so-called ‘proof-of-X’ (PoX) Bano et al. (2019) schemes have been proposed (e.g., proof-of-storage Miller et al. (2014)).

Like in distributed computing, also in social choice theory randomization is an established route to circumvent fundamental impossibility theorems of the deterministic social choice framework, such as the Gibbard-Satterthwaite theorem Gibbard (1973); Satterthwaite (1975).222The theorem states that no social choice function exists which is simultaneously non-manipulable and non-dictatorial. In a famous later theorem Gibbard himself Gibbard (1977) showed how randomization can provide a possibility result that is out of reach in the deterministic setting: the random draw of one agent (the ‘dictator’, or ‘leader’) from the set of agents is the only decision mechanism that is ‘lottery’ strategy-proof (in the specific sense of stochastic dominance333I provide a sketch of the definition here: is the set of agents; is the set of alternatives; is a profile of preferences over . A randomized decision rule is a function , that is, a function assigning a lottery over to each profile of preferences. A lottery stochastically dominates a lottery for iff , for any . A randomized decision rule is strategy-proof, w.r.t. stochastic dominance, if for all it never selects a lottery which is stochastically dominated by another lottery for .

) and ‘lottery’ efficient (in the sense of never assigning positive probability to alternatives that are Pareto dominated). From a blockchain perspective the theorem can be thought to offer a justification for the use of randomization in PoW and PoS consensus: using a lottery to select the next block in the chain is economically efficient and elicits the true preferences of nodes about what block should be included in the chain. A string of works have further extended Gibbard’s result (e.g.,

Gibbard (1977); Procaccia (2010); Aziz et al. (2013)) and randomization is recognized as an important toolbox in the design of economic mechanisms, from allocation to voting Brandt (2017). This body of theory offers a sophisticated framework to understand important economic properties of the sort of lotteries deployed in blockchain protocols. One such property is fairness.

2.2. Challenge: Long-Term Fairness

By linking winning chances to resource ownership and linking lottery outcomes to currency allocation, blockchain protocols make participation resistant to Sybil attacks (participation is costly) and at the same time monetarily rewarding (’no-show’ is disincentivized). This scheme, however, has been shown to induce centralizing effects on several blockchain systems (see, e.g., Kondor et al. (2014); Fanti et al. (2019)). Participants with more resources, all other things being equal, have higher chances of being selected by the lottery and thus accrue more resources in the long term. The resulting allocation of resources invested in the system becomes therefore increasingly unequal over time, and this inequality in resource ownership de facto biases the lotteries upon which consensus is based. In blockchain, such bias translates in a centralization effect, which makes the blockchain more vulnerable to failures or attacks. So, randomized blockchain consensus protocols need to implement, in the long term, allocations of winning chances which are fair towards participating nodes in two somewhat opposing senses: fair in the sense of being lotteries that are not too biased towards few participants, in order to preserve decentralization; and at the same time fair in the sense of being responsive, even proportional, to the resources invested so that participation is suitably incentivized. The analysis of such a trade-off is an inherently social choice-theoretic question: can randomized mechanisms for blockchain be designed which achieve participation incentivization and equitability at the same time, in the long-term? Extensions of existing work in computational social choice may provide the right stepping stone to approach this question, along the following lines.

Perpetual lotteries

First, while randomized mechanisms in social choice are normally studied in one-shot interaction, fairness properties in blockchain should be conceptualized in the context of indefinitely repeating interaction: a lottery may satisfy forms of fairness in one-shot interaction (e.g., assigning winning chances proportionally to invested effort, like in PoW and PoS lotteries) but may fail fairness criteria in the long run (see Fanti et al. (2019)). This suggests the study of randomized mechanisms within the recently developed perpetual voting setting of Lackner (2020) (see also Freeman et al. (2017)). A key feature of the perpetual voting framework that appears particularly relevant for applications in blockchain is, in particular, the history-dependence of decisions. In blockchain this dependence manifests itself via the positive feedback between current and future winning chances. Functions capturing this positive feedback could be approached axiomatically as well as via computer simulations (see Wang et al. (2020) for recent work in this direction) in order to provide a framework to understand long-term fairness properties of blockchain protocols viewed as perpetual randomized mechanisms.

Contest-based lotteries

Second, work on randomized mechanisms in social choice normally assumes uniform probabilities or is agnostic about the specific probability mass functions defining the lotteries. Furthermore, when lotteries are iterated, as in random serial dictatorships Brandt (2017), probability functions do not vary over time. As noticed above, this is not the case in blockchain: an agent’s chance to win equals its share of a total non-monopolizable resource. But there is another crucial element of lotteries in blockchain. The winning probabilities for can be defined as where is ’s invested effort to acquire a non-monopolizable resource (e.g., currency, computing power), and is a function (here assumed unique for all agents for simplicity) mapping each agent’s effort to its acquired amount of resource (see Dimitri (2017)). An agent’s expected utility in this type of interaction is, therefore, That is, ’s probability of winning times its reward (e.g., block reward plus transaction fees in Nakamoto consensus) minus the effort invested. In economics jargon this type of interaction is called a contest Cournot (1838); Tullock (1980); Corchon (2007). Linking contest theory to the make-up of the lotteries in randomized mechanisms would capture a crucial aspect of perpetual randomization in blockchain, and offer a parsimonious framework in which to study long-term fairness properties.

3. Voting

3.1. Voting in Blockchain and Social Choice

Voting mechanisms have been at the heart of distributed computing since its early days (e.g., Garcia-Molina (1982)). Still, almost no crossover has happened between the social choice literature on the analysis of voting mechanisms and the distributed computing literature (a recent exception is Melnyk et al. (2018)). This is perhaps not surprising, as the role that voting plays in the two traditions is fundamentally different. In distributed computing, voting is a consensus mechanism producing agreement in contexts where what matters is agreement itself, and not so much the option upon which agreement settles. That is, the agents involved in consensus are assumed not to be invested in any specific option, but to just aim at reaching consensus. In social choice instead, voting is eminently a mechanism for preference aggregation. Given that blockchains are open systems and that, therefore, agents’ interests cannot be assumed to align, the social choice theoretic perspective on voting becomes naturally relevant.

There are several applications of voting in blockchain, but fork resolution is arguably the main one.444Forks are branches of the blockchain. When these are due to network latency issues or, possibly, attacks—rather than deliberate choices of developers (so-called hard forks)—the protocol is supposed to resolve them. I will illustrate this application of voting with respect to a specific protocol proposed for Ethereum called Casper Buterin and Griffith (2017), although voting mechanisms for fork resolution are used in many systems (e.g., the Spectre protocol Sompolinsky et al. (2017)). In a nutshell, the aim of Casper is to use voting among a randomly selected committee of agents (called validators) to resolve forks in the blockchain and guarantee consensus on a canonical chain (the so-called finality property). Whenever a fork occurs, agents vote on blocks occurring on different branches in the fork (this can be thought of as voting on the nodes of the tree of possible chains). Each agent’s vote is weighted by the agent’s stakes, that is, the agent’s deposit in currency (so, a high deposit means greater voting power), and a block is considered to belong to the canonical chain whenever a weighted supermajority of votes for that block. This voting procedure guarantees that the winning blocks identify a legitimate chain (i.e., without forks), provided that the agents submitting individually consistent votes (that is, not voting for blocks on different chains) own at least of the total deposits.

3.2. Challenge: Manipulating Byzantine Voting

Voting procedures are vulnerable to manipulations of different kinds: strategic voting Taylor (2005), lobbying Christian et al. (2007), bribery and control Faliszewski and Rothe (2016), vote negotiation Grandi et al. (2019). Given the incentives layer of blockchain protocols, all such forms of vote manipulation are potentially relevant in view of the deployment of voting mechanisms. For example, returning to Casper, although the protocol can be shown to be robust against a share of Byzantine voters worth of the total deposit in stakes, to what extent is the protocol robust against strategic forms of vote manipulation of the types mentioned above? More generally: to what extent should voting mechanisms in blockchain consensus be robust against forms of vote manipulation?

Given that voting in blockchain systems is conducted by computational processes, the computational complexity approach to robustness against manipulations appears especially natural: robustness to manipulations pursued through computational intractability Bartholdi et al. (1989); Faliszewski and Rothe (2016)

. In this perspective, one might argue more specifically that voting mechanisms for blockchain should satisfy two properties: have a tractable winner determination problem; have intractable manipulation problems with respect to forms of manipulation that, given the application, may be considered relevant. Results from the above mentioned literature offer an obvious starting point, but should be extended in order to incorporate the possibility—which is fundamental in the distributed computing perspective—of Byzantine agents, in a way akin to what has been pursued in applications of game theory to distributed computing (see, for instance, the so-called Byzantine-Altruistic-Rational fault-tolerance models

Clement et al. (2007)). In particular, the decision problems themselves concerning the existence of manipulation strategies would need to be adjusted to this setting, by allowing for the possibility of shares of the agents population to be Byzantine.

4. Trust

4.1. Trust in Blockchain and Social Choice

Among the key limitations of PoW are its high energy demand,555

The estimated annual energy consumption of the Bitcoin network is 194.95 TWh, roughly comparable to the annual energy consumption of a country like Thailand. Source: digiconomist.net (last accessed on 19.11.21).

high latency and low transactions throughput Bonneau et al. (2015). An influential approach trying to address these limitations has been proposed by blockchain systems like Stellar Mazierès (2016) and Ripple Schwartz et al. (2014)666They represent, respectively, the 7th and 24th cryptocurrency in terms of market capitalization (in the order of hundreds of millions of dollars). Source: coinmarketcap.com (last accessed on 19.11.21). or TrustChain Otte et al. (2017). The approach of these systems to safeguard consensus against Sybil attacks is not based on lotteries but on the idea of leveraging existing ‘real-world’ trust relations in order to select the agents that may participate in consensus. In other words, the system remains open, but new participants are admitted only if trusted by existing ones. According to the proponents of these systems, this should make it possible then to use well-established consensus approaches proper of permissioned (i.e., closed) systems, like Byzantine fault-tolerant consensus (BFT, Lamport et al. (1982); Castro and Liskov (1999)). Nodes participate in consensus, but only in as much as they are trusted by others. This controls participation to the consensus process by restricting access. It does so, however, in a way that is in principle open and decentralized.

Abstractly, the above systems work on the basis of an underlying trust network that links nodes according to who trusts whom. At any given time, each honest node broadcasts a truthful opinion about the state of the next block (e.g., whether a given block should be included or not) to the nodes that listen to it. But the system may contain Byzantine nodes, and such nodes may reveal different opinions to different honest nodes. A consensus protocol running on such a trust network can be viewed as a discrete time dynamical system generating a stream of opinion vectors of nodes. The final vector should be such that all honest nodes hold the same opinion, that is, the system does not fork—the so-called ‘safety’ property.

At least three strands of research in computational social choice appear relevant for the above class of systems. The first one is the axiomatic and computational analysis of trust and reputation mechanisms (e.g., Ghosh et al. (2007); Seuken et al. (2010); Tennenholtz and Zohar (2013)). The second one is the analysis of influence and power in structured groups and social networks (e.g., Hu and Shapley (2003b, a); Grabisch and Rusinowska (2011)). The third one is the analysis Sybil-proofness, or false-name proofness (e.g., Conitzer and Yokoo (2010); Todo et al. (2011); Waggoner et al. (2012)). In what follows I will outline how especially the latter two strands of research can offer insights into the fundamental tradeoffs between decentralization, safety and sybil-proofness that the above systems need to handle.

4.2. Challenge: Decentralized Sybil-proof Trust

Understanding how to deploy BFT consensus in a permissionless setting is explicitly recognized as an open problem in distributed computing Cachin and Vukolic (2017); Vukolic (2015). Yet, little academic research exists on the trust-based approach to consensus used by systems like Ripple and Stellar. Computational social choice could provide a fruitful framework from which to study this approach: Can trust systems for blockchain consensus be designed that maintain safety (i.e., absence of forks) are decentralized and, at the same time, Sybil-proof?

Decentralization & safety

Trust involves a form of influence: a node’s voting decision on whether to validate a block depends on the decisions of the nodes it trusts and ‘listens to’. At the same time, safety demands that no two honest nodes express dissenting (finalized) votes and this in turn imposes structural properties on the trust structure: if we do not want forks to occur, then trust structures should satisfy specific properties (see Mazierès (2016); Bracciali et al. (2020)). But how decentralized a system really is when such properties hold is unclear, because some nodes may end up accruing disproportionate influence in the network. De facto centralization is a well-known phenomenon in PoW and PoS blockchains (see the above discussion about randomized mechanisms) but a comparable understanding for consensus protocols based on trust mechanisms is still lacking. In particular it is unclear how to even quantify influence on the consensus process in such systems, although some proposals have been put forth using the theory of power indices Bracciali et al. (2020).

Sybil-proofness of trust mechanisms

If consensus is based on trust systems like the ones sketched above, what kind of Sybil-proofness guarantees can be achieved? Intuitively, trust relations should make the system harder to access for Sybils as they would be able to exercise influence on consensus only if trusted by honest nodes. But can this argument be made exact?

PoW and PoS protocols implement a form of costly identity. They make participation to consensus costly by making it dependent on the investment in a resource (e.g., computing power). In a way nodes purchase identities on a continuum and proportionally to their ownership of a non-monopolizable resource. Costly identities have been investigated also in social choice and mechanism design as one possible approach to achieve the so-called false-name-proofness of a mechanism. A mechanism is said to be false-name-proof if no agent participating in it would benefit by using more than one identifier to interact with the mechanism. A number of routes to enforce false-name-proofness have been investigated in this literature and costly identities have been studied also in the context of voting Wagman and Conitzer (2008).777Intuitively, a voting mechanism is then false-name-proof if the cost of casting additional votes always exceeds the gains an agent would obtain by doing so. In this context, while creating Sybils may be costless, creating trustworthy ones can be made costly. The issue then translates into understanding the tradeoffs that manipulators face between identifiers’ costs and their payoffs measured in terms of expected influence on the consensus process.

5. Conclusions

This paper has highlighted how the applications to blockchain of mechanisms such as lotteries, voting or trust systems give rise to challenges that have a natural social choice dimension. These challenges all revolve around understanding fundamental tradeoffs, often in the long run, among properties that are crucial to the correct behavior of blockchain consensus protocols and are linked to the incentive dimensions of such protocols. In pursuing such problems from a computational social choice perspective, one would need to adapt standard concepts, definitions and techniques to the blockchain setting. This adaptation opens up promising lines of research and this paper has tried to illustrate some such lines, which appear promising to the author.

What covered, however, should not be considered exhaustive. In particular, this paper has focused on the problem of consensus, but looking more broadly at the blockchain field one finds many more points of contact with social choice, some of which have already been identified in the literature. For example, voting theory and coalitional games have been applied to the problem of the algorithmic governance of hard forks in blockchain Abramowitz et al. (2021), and epistemic social choice has been applied to the so-called oracle problem Goel et al. (2020); Cai et al. (2020), that is, how to reliably link blockchain records to real-world events. For all these reasons I believe there exists now a deep cross-fertilization potential between the two areas of research, and one that would greatly benefit both.

I thank the anonymous reviewers for their helpful comments.

References

  • (1)
  • Abraham et al. (2011) I. Abraham, L. Alvisi, and J. Halpern. 2011. Distributed Computing Meets Game Theory: Combining Insights from Two Fields. ACM Sigact News 42, 2 (2011), 69–76.
  • Abraham et al. (2016) I. Abraham, D. Malkhi, K. Nayak, L. Ren, and A. Spiegelman. 2016. Solidus: An Incentive-Compatible Cryptocurrency Based on Permissionless Byzantine Consensus. Technical Report. arXiv:1612.02916.
  • Abramowitz et al. (2021) B. Abramowitz, E. Elkind, D. Grossi, E. Shapiro, and N. Talmon. 2021. Democratic Forking: Choosing Sides with Social Choice. In Algorithmic Decision Theory - 7th International Conference, ADT 2021, Toulouse, France, November 3-5, 2021, Proceedings. 341–356.
  • Alkalay-Houlian and Shah (2019) C. Alkalay-Houlian and N. Shah. 2019. The Pure Price of Anarchy of Pool Block Withholding Attacks in Bitcoin Mining. In

    Proceedings of The Thirty-Third AAAI Conference on Artificial Intelligence, AAAI 2019

    . AAAI Press.
  • Amoussou-Guenou et al. (2020) Y. Amoussou-Guenou, B. Biais, M. Potop-Butucaru, and S. Tucci Piergiovanni. 2020. Rational vs Byzantine Players in Consensus-based Blockchains. In Proceedings of the 19th International Conference on Autonomous Agents and Multiagent Systems, AAMAS. IFAAMAS, 43–51.
  • Aziz et al. (2013) H. Aziz, F. Brandt, and M. Brill. 2013. On the Tradeoff between Economic Efficiency and Strategyproofness in Randomized Social Choice. In Proceedings of AAMAS’13. 455–462.
  • Bano et al. (2019) S. Bano, A. Sonnino, M. Al-Bassam, S. Azouvi, P. McCorry, S. Meiklejohn, and G. Danezis. 2019. SoK: Consensus in the Age of Blockchain. In Proceedings of the 1st ACM Conference on Advances in Financial Technologies, AFT 2019. ACM, 183–198.
  • Bartholdi et al. (1989) J. Bartholdi, C. Tovey, and M. Trick. 1989. The Computational Difficulty of Manipulating an Election. Social Choice and Welfare 6, 3 (1989), 227–241.
  • Bonneau et al. (2015) J. Bonneau, A. Miller, J. Clark, A. Narayanan, J. Kroll, and E. Felten. 2015. Sok: Research Perspectives and Challenges for Bitcoin and Cryptocurrencies. In 2015 IEEE Symposium on Security and Privacy (SP’15). 104–121.
  • Bracciali et al. (2020) A. Bracciali, D. Grossi, and R. de Haan. 2020. Decentralization in Open Quorum Systems: Limitative Results for Ripple and Stellar. In 2nd International Conference on Blockchain Economics, Security and Protocols, Tokenomics 2020. 1–20.
  • Brandt (2017) F. Brandt. 2017. Rolling the Dice: Recent Results in Probabilistic Social Choice. In Trends in Computational Social Choice, U. Endriss (Ed.). AI Access, 3–26.
  • Buterin (2013) V. Buterin. 2013. A Next Generation Smart Contract and Decentralized Application Platform. (2013). https://github.com/ethereum/wiki/wiki/White-Paper.
  • Buterin and Griffith (2017) V. Buterin and V. Griffith. 2017. Casper the Friendly Finality Gadget. Technical Report. Ethereum Foundation, arXiv:1710.09437.
  • Cachin and Vukolic (2017) C. Cachin and M. Vukolic. 2017. Blockchain Consensus Protocols in the Wild. Technical Report. CoRR abs/1707.01873.
  • Cai et al. (2020) Y. Cai, G. Fragkos, E.-E. Tsiropoulou, and A. G. Veneris. 2020. A Truth-Inducing Sybil Resistant Decentralized Blockchain Oracle. In 2nd Conference on Blockchain Research & Applications for Innovative Networks and Services, BRAINS 2020. IEEE, 128–135.
  • Castro and Liskov (1999) M. Castro and B. Liskov. 1999. Practical Byzantine Fault Tolerance. In Proceedings of the 3rd Symposium on Operating Systems Desgin and Implementation. 173–186.
  • Chen et al. (2021) L. Chen, L. Xu, Z.Gao, A. I. Sunny, K. Kasichainula, and W. Shi. 2021. A Game Theoretical Analysis of Non-Linear Blockchain System. In AAMAS ’21: 20th International Conference on Autonomous Agents and Multiagent Systems. ACM, 323–331.
  • Christian et al. (2007) R. Christian, M. Fellows, F. Rosamond, and A. Slinko. 2007. On complexity of lobbying in multiple referenda. Review of Economic Design 11, 3 (2007), 217–224.
  • Clement et al. (2007) A. Clement, J. Napper, H. Li, J.-P. Martin, L. Alvisi, and M. Dahlin. 2007. Theory of BAR games. In Proceedings of PODC’07. 358–359.
  • Conitzer and Yokoo (2010) V. Conitzer and M. Yokoo. 2010. Using Mechanism Design to Prevent False-Name Manipulations. AI Magazine 31, 4 (2010), 65–77.
  • Corchon (2007) L. Corchon. 2007. The Theory of Contests: A Survey. Review of Economic Design 11 (2007), 69–100.
  • Cournot (1838) A. Cournot. 1838. Recherches sur le Pronciples Mathematiques de la theorie des Richesses. Hachette, Paris.
  • Daian et al. (2016) P. Daian, Pass. R., and E. Shi. 2016. Snow White: Provably Secure Proofs of Stake. Technical Report 2016/919. Cryptology ePrint Archive.
  • David et al. (2017) B. David, P. Gazi, A. Kiayias, and A. Russell. 2017. Ouroboros Praos: An Adaptively-Secure, Semi-Synchronous Proof-of-Stake Protocol. Technical Report 2017/573. Cryptology ePrint Archive.
  • Dimitri (2017) N. Dimitri. 2017. Bitcoin Mining as a Contest. Ledger 2 (2017), 31–37.
  • Douceur (2002) J. Douceur. 2002. The Sybil Attack. In First International Workshop on Peer-to-Peer Systems. 251–260.
  • Dwork and Naor (1992) C. Dwork and M. Naor. 1992. Pricing via processing for combatting junk mail. In Advances in Cryptology - CRYPTO’92, Vol. 740. 139–147.
  • Eyal (2015) I. Eyal. 2015. The Miner’s Dilemma. In IEEE symposium S&P’15. 89–103.
  • Faliszewski and Rothe (2016) P. Faliszewski and J. Rothe. 2016. Control and Bribery in Voting. In Handbook of Computational Social Choice, F. Brandt, V. Conitzer, U. Endriss, J. Lang, and A. Procaccia (Eds.). Cambridge University Press, Chapter 7, 146–168.
  • Fanti et al. (2019) G. C. Fanti, L. Kogan, S. Oh, K. Ruan, P. Viswanath, and G. Wang. 2019. Compounding of Wealth in Proof-of-Stake Cryptocurrencies. In Financial Cryptography and Data Security - 23rd International Conference, FC 2019. 42–61.
  • Fischer et al. (1985) M. Fischer, N. Lynch, and Paterson M. 1985. Impossibility of Distributed Consensus with one Faulty Process. J. ACM 32, 2 (1985), 374–382.
  • Freeman et al. (2017) R. Freeman, S. M. Zahedi, and V. Conitzer. 2017. Fair and Efficient Social Choice in Dynamic Settings. In Proceedings of the 26th International Joint Conference on Artificial Intelligence (IJCAI’17). 4580–4587.
  • Garay et al. (2015) J. Garay, A. Kiayias, and Nikos L. 2015. The Bitcoin Backbone Protocol: Analysis and Applications. In Advances in Cryptology - EUROCRYPT 2015, E. Oswald and M. Fischlin (Eds.). Springer.
  • Garcia-Molina (1982) H. Garcia-Molina. 1982. Elections in a Distributed Computing System. In IEEE Transactions on Computers, Vol. 31.
  • Ghosh et al. (2007) A. Ghosh, M. Mahdian, D. Reeves, D. Pennock, and R. Fugger. 2007. Mechanism Design on Trust Networks. In Proceedings of the 3rd International Workshop On Internet And Network Economics (WINE 2007) (LNCS, 4858). Springer.
  • Gibbard (1973) A. Gibbard. 1973. Manipulation of Voting Schemes: A General Result. Econometrica 41, 4 (Jul. 1973), 587–601.
  • Gibbard (1977) A. Gibbard. 1977. Manipulation of Schemes that Mix Voting with Chance. Econometrica 45, 3 (1977).
  • Gilad et al. (2017) Y. Gilad, R. Hemo, S. Micali, G. Vlachos, and N. Zeldovich. 2017. Algorand: Scaling Byzantine Agreements for Cryptocurrencies. In Proceedings of SOSP’17.
  • Goel et al. (2020) N. Goel, C. van Schreven, A. Filos-Ratsikas, and B. Faltings. 2020. Infochain: A Decentralized, Trustless and Transparent Oracle on Blockchain. In Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence, IJCAI 2020, Christian Bessiere (Ed.). 4604–4610.
  • Grabisch and Rusinowska (2011) M. Grabisch and A. Rusinowska. 2011. Influence Functions, Followers and Command Games. Games and Economic Behavior 72, 1 (2011), 123–138.
  • Grandi et al. (2019) U. Grandi, D. Grossi, and P. Turrini. 2019. Negotiable Votes. Pre-Vote Negotiations in Binary Voting with Non-Manipulable Rules. Journal of Artificial Intelligence Research 64 (2019), 895–929.
  • Hu and Shapley (2003a) X. Hu and L. Shapley. 2003a. On Authority Distributions in Organizations: Controls. Games and Economic Behavior 45 (2003), 153–170.
  • Hu and Shapley (2003b) X. Hu and L. Shapley. 2003b. On Authority Distributions in Organizations: Equilibrium. Games and Economic Behavior 45 (2003), 132–152.
  • Judmayer et al. (2021) A. Judmayer, N. Stifter, A. Zamyatin, I. Tsabary, I. Eyal, P. Gazi, S. Meiklejohn, and E. R. Weippl. 2021. SoK: Algorithmic Incentive Manipulation Attacks on Permissionless PoW Cryptocurrencies. In Financial Cryptography and Data Security. FC 2021 International Workshops - CoDecFin, DeFi, VOTING, and WTSC, Virtual Event, March 5, 2021, Revised Selected Papers (Lecture Notes in Computer Science, Vol. 12676), M. Bernhard, A. Bracciali, L. Gudgeon, T. Haines, A. Klages-Mundt, S. Matsuo, D. Perez, M. Sala, and S. Werner (Eds.). Springer, 507–532.
  • Kiayias et al. (2017) A. Kiayias, A. Russell, B. David, and Oliynykov. 2017. Ouroboros: A Provably Secure Proof-of-Stake Blockchain Protocol. In Proceedings of CRYPTO’17.
  • Kondor et al. (2014) D. Kondor, M. Posfai, I. Csabai, and G. Vattay. 2014. Do the Rich Get Richer? An Empirical Analysis of the Bitcoin Transaction Network. PLoS ONE 9, 5 (2014).
  • Lackner (2020) M. Lackner. 2020. Perpetual Voting: Fairness in Long-Term Decision Making. In The Thirty-Fourth AAAI Conference on Artificial Intelligence, AAAI 2020. 2103–2110.
  • Lamport et al. (1982) L. Lamport, R. Shostak, and M. Pease. 1982. The Byzantine Generals Problem. ACM Transactions on Programming Languages and Systems 4, 3 (1982), 382–401.
  • Mazierès (2016) D. Mazierès. 2016. The Stellar Consensus Protocol: A Federated Model for Internet-level Consensus. (2016). Stellar Development Foundation.
  • Melnyk et al. (2018) D. Melnyk, Y. Wang, and R. Wattenhofer. 2018. Byzantine Preferential Voting. In Proceedings of 3rd Highlight of Algorithms (HALG’18).
  • Miller et al. (2014) A. Miller, Juels. A., E. Shi, B. Parno, and J. Katz. 2014. Permacoin: Repurposing Bitcoin Work for Data Preservation. In Proceedings of the 2014 IEEE Symposium on Security and Privacy. IEEE, 475–490.
  • Nakamoto (2008) S. Nakamoto. 2008. Bitcoin: A Peer-to-Peer Electronic Cash System. (2008). https://bitcoin.org/bitcoin.pdf.
  • Narayanan et al. (2016) A. Narayanan, J. Bonneau, E. Felten, A. Miller, and S. Goldfeder. 2016. Bitcoin and Cryptocurrency Technologies. Princeton University Press.
  • Otte et al. (2017) P. Otte, M. de Vos, and J. Pouwelse. 2017. TrustChain: A Sybil-resistant scalable blockchain. Future Generation Computer Systems (2017).
  • Procaccia (2010) A. Procaccia. 2010. Can Approximation Circumvent Gibbard-Satterthwaite. In Proceedings of AAAI’10. 836–841.
  • Sapirstein et al. (2016) A. Sapirstein, Y. Sompolinsky, and A. Zohar. 2016. Optimal Selfish Mining Strategies in Bitcoin. In Proceedings of Financial Cryptography and Data Security 2016 (FC’16).
  • Satterthwaite (1975) M. A. Satterthwaite. 1975. Strategy-proofness and Arrow’s conditions: Existence and correspondence theorems for voting procedures and social welfare functions. Journal of Economic Theory 10, 2 (April 1975), 187–217.
  • Schwartz et al. (2014) D. Schwartz, N. Youngs, and A. Britto. 2014. The Ripple Protocol Consensus Algorithm. Technical Report. Ripple Labs.
  • Seuken et al. (2010) S. Seuken, J. Tang, and D. Parkes. 2010. Accounting Mechanisms for Distributed Work Systems. In Proceedings of the AAAI’10. AAAI Press.
  • Sompolinsky et al. (2017) Y. Sompolinsky, Y. Lewenberg, and A. Zohar. 2017. SPECTRE: Serialization of Proof-of-Work Events: Confirming Transactions via Recoursive Elections. Technical Report. IACR ePrint archive.
  • Sompolinsky and Zohar (2018) Y. Sompolinsky and A. Zohar. 2018. Bitcoin’s Underlying Incentives. Commun. ACM 81, 3 (2018), 46–53.
  • Taylor (2005) A. D. Taylor. 2005. Social Choice and the Mathematics of Manipulation. Cambridge University Press.
  • Tennenholtz and Zohar (2013) M. Tennenholtz and A. Zohar. 2013. The Axiomatic Approach and the Internet. In Handbook of Computational Social Choice. Cambridge University Press.
  • Todo et al. (2011) T. Todo, A. Iwasaki, and M. Yokoo. 2011. False-Name-Proof Mechanism Design Without Money. In Proceedings of AAMAS’11. IFAAMAS, 651–658.
  • Tullock (1980) G. Tullock. 1980. Efficient Rent Seeking. In Towards a Theory of Rent Seeking Society, J. Buchanan, R. Tollison, and G. Tullock (Eds.). Texas A&M Press.
  • Vukolic (2015) M. Vukolic. 2015. The Quest for Scalable Blockchain Fabric: Proof-of-Work vs. BFT Replication. In Proceedings of iNetSec’15 (LNCS, Vol. 9591). 112–125.
  • Waggoner et al. (2012) B. Waggoner, L. Xia, and V. Conitzer. 2012. Evaluating Resistance to False-Name Manipulations in Elections. In Proceedings of AAAI’12. 1485–1491.
  • Wagman and Conitzer (2008) L. Wagman and V. Conitzer. 2008. Optimal false-name proof voting rules with costly voting. In AAAI’08. 190–195.
  • Wang et al. (2020) Y. Wang, G. Yang, A. Bracciali, H. Leung, H. Tian, L. Ke, and X. Yu. 2020. Incentive compatible and anti-compounding of wealth in proof-of-stake. Information Sciences 530 (2020), 85–94.
  • Wattenhofer (2017) R. Wattenhofer. 2017. Distributed Ledger Technology: The Science of the Blockchain. Createspace Independent Publishing Platform.