Astraea: A Decentralized Blockchain Oracle

08/01/2018 ∙ by John Adler, et al. ∙ UNIVERSITY OF TORONTO Athens University of Economics and Business 0

The public blockchain was originally conceived to process monetary transactions in a peer-to-peer network while preventing double-spending. It has since been extended to numerous other applications including execution of programs that exist on the blockchain called "smart contracts." Smart contracts have a major limitation, namely they only operate on data that is on the blockchain. Trusted entities called oracles attest to external data in order to bring it onto the blockchain but they do so without the robust security guarantees that blockchains generally provide. This has the potential to turn oracles into centralized points-of-failure. To address this concern, this paper introduces Astraea, a decentralized oracle based on a voting game that decides the truth or falsity of propositions. Players fall into two roles: voters and certifiers. Voters play a low-risk/low-reward role that is resistant to adversarial manipulation while certifiers play a high-risk/high-reward role so they are required to play with a high degree of accuracy. This paper also presents a formal analysis of the parameters behind the system to measure the probability of an adversary with bounded funds being able to successfully manipulate the oracle's decision, that shows that the same parameters can be set to make manipulation arbitrarily difficult---a desirable feature for the system. Further, this analysis demonstrates that under those conditions a Nash equilibrium exists where all rational players are forced to behave honestly.



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I Introduction

Blockchain technology was originally developed to handle monetary transactions in the form of a digital currency using a peer-to-peer network while solving the double spending problem [1]. In its original application, it allowed a set of anonymous and mutually-distrusting entities to reach consensus on the order of a set of such transactions. In recent years this concept has been extended to other domains in a way that enables such parties to reach consensus on items such as the order of private monetary transactions [2, 3], the responsibility for file storage in a peer-to-peer network [4], the sequence of executed states in generalized computations [5], and more.

A major limitation of blockchain technology is its inability to interact with the “outside world” [6, 7]. For example, in Ethereum [5] the network can reach consensus on the outcome of a sequence of computations. However, these computations can only operate on data that is on the blockchain, that is, a prior computation initiated by a user of Ethereum wrote the relevant data into the virtual machine’s memory. The network does not natively support reaching consensus on the validity of such data, only the fact that it exists on the blockchain can be agreed upon. As such, trusted entities called oracles are needed to attest to facts in an effort to bring external data into the consensus mechanism of a blockchain. Generally speaking, such oracles do not provide the robust security properties of native blockchain protocols. This may not be a substantial limitation when the external data can be proven correct either cryptographically (such as data that comes from another blockchain [8, 9]), or computationally (such as the outcomes of complex computations that are infeasible to perform on platforms such as Ethereum [10]). However, facts that cannot be provably verified like the ones above present unique challenges for existing oracles.

TLSnotary [11] and TownCrier [12] are oracles that provide cryptographically-checkable information as they attest to the content of websites accessed using the Hypertext Transfer Protocol Secure (HTTPS) protocol. The underlying idea behind these oracles is that attestations are checkable due to the use of transport layer security (TLS). However, TLS does not guarantee that every visitor to the site sees the same information. Additionally, a website could maliciously alter its output to influence on-chain attestations, creating a centralized point-of-failure in the system. TownCrier uses Intel Software Guard Extensions in order to protect the attestations against a malicious operating system. In the case of Augur [13], it uses an oracle to determine the outcome of events so as to pay out participants in a prediction market. The oracle may require specific users to report outcomes at specific times or face a monetary penalty. As such, users who maliciously report incorrect results may be subject to a dispute process. While offering greater decentralization, Augur’s oracle does not offer users the opportunity to drop in and out of the system at will which is somewhat harmful to the usability of the ecosystem.

In this work, we propose Astraea—a general-purpose decentralized oracle that runs on a public ledger and leverages human intelligence through a voting-based game. Without loss of generality, we describe our contributions using the Ethereum blockchain but other platforms with similar smart contract characteristics can be utilized as the underlying decentralized network. Entities in Astraea can fall into one or more of three roles: submitters, voters, and certifiers. Submitters submit Boolean propositions to the system and pay fees for doing so. Voters play a low-risk/low-reward game where they are given the opportunity to vote on the truth of a random proposition by placing a “small” stake in their confidence of their vote being correct. Certifiers play a high-risk/high-reward game where they place a “large” stake on the outcome of the voting and certification process. For usability, voters and certifiers are not required to be online during particular time periods; all roles may enter or exit the system at any time. Due to its requirement for monetary staking and fees, the system is inherently not vulnerable to Sybil attacks [14].

In more detail, in Astraea voters place a small amount of stake and are given the opportunity to vote on a proposition selected randomly from the system. This stake is deposited before seeing the proposition. The outcome of voting is the stake-weighted sum of votes. Due to the randomness involved when selecting a proposition, voting is resistant to manipulation by actors seeking to force an incorrect result for a particular proposition. On the other hand, certifiers place large stakes on the truth or falsity of propositions of their choosing. Similar to voting, the outcome of certification is the stake-weighted sum of certifications. However, not all propositions necessarily carry certifications. Nevertheless, when one exists and the voter outcome matches that of the certifier, players who took the corresponding position are rewarded and players who took the opposing position are penalized. When the voter and certifier outcomes disagree, all of the certifiers who took a position are penalized. It is important to note that votes and certifications are sealed and revealed only at the end of the aforementioned process. Intuitively, the proposed system encourages certifiers to place bets on propositions for which there is a high degree of confidence that they are true or false, and it also encourages voters to vote accurately on the propositions they are randomly given.

Analysis reveals that the proposed system has desirable properties. In this paper, we determine the probability of an adversary manipulating the voting outcome and we demonstrate that system parameters can be chosen in a way so that an adversary with a bounded amount of funds also has an arbitrarily small probability of successfully manipulating it. Further, we demonstrate that under the same conditions that prevent an adversary from manipulating voting, the system has a Nash equilibrium in which all players play honestly. Finally, we argue that the certification process avoids degenerate coordination strategies in which users always vote with a constant “true” or “false” without regard to the validity of the actual proposition so as to earn a profit.

The remainder of this paper is outlined as follows. Section II gives a brief overview of blockchains, oracles, and key assumptions. Section III follows with a summary of current blockchain oracle projects. Sections IV and V introduce Astraea and analyze it from a game-theoretical direction. An extension to Astraea is presented in Section VI. Finally, applications of a decentralized oracle are shown in Section VII.

Ii Preliminaries and System Assumptions

Ii-a The Distributed Public Ledger

Bitcoin [1] is a blockchain-based distributed ledger of monetary transactions which transfers coins between users identified by their public keys and certified by digital signatures. Transactions are grouped into blocks which are ordered lists of transactions. Each block contains a hash that commits to the previous block, forming a hash-linked chain (i.e., a blockchain). An unambiguous head of the chain determines the precise order in which transactions occurred, preventing double-spending. Bitcoin’s [1] primary innovation was the use of Proof-of-Work (PoW) to reach consensus on the head of the chain. Miners combine transactions into blocks. Each block has a header consisting of a hash of its own transactions, a hash of the previous block header, and a nonce used for PoW. Users select as the head the block with the most cumulative work in its history. Rewriting the chain to undo a transaction requires repeating PoW, and the further back in history the transaction is, the more work is required.

Ethereum [5] uses similar ideas to generalize consensus on the state of a virtual Turing-complete computer. Ethereum transactions may additionally insert a smart contract [15] into the virtual machine or call a function of an existing contract thus extending the applicability and usability of a blockchain.

Ii-B Oracles

This work focuses on a particular issue facing smart contracts: their inability to act on data that exists outside the blockchain. Smart contract execution must be deterministic in order to be publicly verifiable in perpetuity. As such, they cannot directly pull data from e.g., the Internet. For example, consider a contract to allow wagers on the outcome of the Mayweather vs McGregor boxing match [16]. It would be straightforward to devise a smart contract that pays out bettors based on a flag representing the outcome of the match, but trustlessly determining the value of that flag is a major challenge. In that sense, oracles allow a blockchain to interact with the real, outside world.

Ii-C System Assumptions

This paper presents Astraea, an oracle that decides the truth value of Boolean propositions. We assume each proposition has a truth value that is either true () or false (). There are players (voters and certifiers) numbered through . For each proposition and each , let denote the belief of player regarding the truth value of proposition . Each player has an accuracy that is, informally, the probability that player is correct about a given proposition. Formally:


The value of is independent of for all . That is, each player’s beliefs are independent of all other players’ beliefs. Entities that have non-independent beliefs (e.g., users that pool their voting efforts in the style of mining pools [17]) are treated as a single player. Further is independent of for all . That is, a player’s belief in a proposition is independent of her beliefs in all other propositions. An honest player always votes or certifies that proposition has truth value .

Iii Prior Art

The challenge of smart contracts interacting with the outside world has spawned numerous oracle proposals with varying degrees of centralization, performance, and scope tradeoffs. A brief description of previous work is found here.

Iii-a Existing Blockchain Oracle Proposals

Hivemind (previously Truthcoin) [18] is a prediction marketplace built upon Bitcoin. It allows users to report on the predicted outcome of a future event by staking reputation currency, while traders trade on the event’s market using base currency (i.e., Bitcoin). However, it requires a complex scheme to balance incentives involving two currencies and it has a permissioned and centralized implementation due to token distribution limitations. Augur [13] is a prediction market platform built upon Ethereum, heavily inspired by Truthcoin.

Gnosis [19] and its fork Delphi [20] are also prediction markets built upon Ethereum. Both suffer from a gameable dispute resolution design and centralized token distribution. ChainLink [21] aims to provide a cross-chain portal to internet-available information i.e., data available on websites, through their centralized system. [22] is a centralized platform that creates trusted blockchain transactions for use in smart contracts [16].

Town Crier [12] uses a stack of trusted hardware and software, and publishes proofs that this computational stack has not been tampered with. This system is highly effective, so long as users trust that the underlying hardware does not contain backdoors or exploits [23, 24]. In effect, the validity and accuracy of the protocol depends on a central authority.

All in all, the need of oracles to assist smart contracts was identified shortly after blockchain technology came into existence but no truly decentralized, trustless, and permissionless solution has been presented until this work.

Iv Astraea

This section presents the decentralized voting-based oracle Astraea. It begins with a high-level overview of the user roles and the operation of the voting game and concludes with a detailed description of the game. The next section analyzes the coordination game, illustrates its properties, and demonstrates a desirable Nash equilibrium.

Iv-a Overview

Users of Astraea participate in one (or more) of the following three roles: submitters, voters, and certifiers, that behave as follows.

  • Submitters choose which propositions enter into the system by allocating money to fund (in part) the subsequent effort to validate the Boolean propositions.

  • Voters play a low-risk/low-reward role. Once such a player submits a deposit (stake), she is given the chance to vote on a proposition chosen uniformly at random from the ones available. The stake is placed before the voter is notified of which proposition she will be voting on. The steps of this process are depicted in Figure 1. The outcome of the voting process is a function of the sum of the votes weighted by the deposits. The maximum voting deposit is a parameter of the system.

  • Certifiers play a high-risk/high-reward role. They choose an available proposition and place a large deposit in order to certify it as either true or false. The certification outcome is a function of the sum of certifications weighted by the deposits. This process is depicted in Figure 2. Since certifiers choose which propositions to certify, not all propositions are guaranteed to have certification, and indeed the system does not mandate them to do so. The minimum certification deposit size is a system parameter and should be large enough that certifying incurs a substantial risk.

Setting the parameters appropriately is important for the functionality of the system. The maximum voting deposit size should be small relative to the total voting stake on each proposition. If a single vote can account for 100% of a proposition’s total voting stake, an adversary can have total control over the outcome of a randomly drawn proposition. Conversely, if it is 1%, the adversary would somehow need to draw the same proposition repeatedly to control its validity outcome. On the other hand, the minimum certification deposit should be large enough that certifiers incur sufficient risk. Otherwise, they may be tempted to abuse their certifications for griefing purposes as a malicious certification can impact reward payouts for other players. At first sight, it seems like individual certifiers have enormous influence on the process for individual propositions, and indeed this can be the case. However, as described later in the paper, the certifiers alone cannot force the oracle to produce an incorrect value and they are encouraged to behave honestly by the incentive structure; otherwise they face large penalties.

Fig. 1: Player voting in Astraea
Fig. 2: Player certifying in Astraea

Iv-B The Proposition List

A key aspect of the system is the set of propositions over which voters and certifiers play the game. We assume that there exists a set of propositions constructed outside of Astraea called the proposition list, which is denoted by and is of fixed size . Each proposition has a hidden truth value and is associated with a bounty amount , the source of which is described later. The voting game described later is played over all propositions in simultaneously. In addition, we assume there are two certifier reward pools containing and monetary units, intended to reward certifiers for true and false outcomes, respectively. The use of two separate reward pools is intended to avoid a degenerate coordination strategy in which users always vote and certify with a constant true or false so as to maximize their profit without expending any effort and its rationale is justified later in this paper.

The proposition list can be constructed in a variety of ways and it is outside the scope of this paper. For instance, an auction could be conducted for the spaces, with the auction prices becoming the bounty for each proposition.

After reaching a termination condition, propositions are decided, at which point the game outcome is computed, the proposition is removed from the list, and the corresponding rewards and penalties are administered. A proposition is decided after it has received a certain amount of voting stake denoted , which is the same for all propositions. The proposition can then be replaced with a new one by, for instance, conducting another auction.

Iv-C System Description

For each of the players, denotes the amount that player has staked on voting that proposition is where . If player has not voted on proposition , then and are both equal to . Otherwise, one or both (in the case where player has voted more than once in differing directions) are nonzero and equal to the stake with which they voted. Additionally, let denote the amount of stake that player used to certify that proposition is . Let and denote the maximum voting stake and minimum certifying stake parameters, respectively.

An overview of the game architecture is shown in Figure 3. It depicts a set of players who are either voters, certifiers, or both. In that figure, the differing mechanisms of interaction with the propositions can also be seen. Voters must engage in a multi-step process in order to vote on random propositions, while certifiers simply submit a certification to a proposition of their choosing in one step.

Fig. 3: Overview of Astraea

Iv-C1 Voting

Players may place a deposit in order to vote on a randomly-chosen proposition. First, the voter indicates a desire to stake an amount of money on a vote for proposition , where is not yet known to the voter. Subsequently, the system chooses the value for and sends it to the voter. Note that is chosen uniformly at random from , so a voter may be given the opportunity to vote on the same proposition more than once. Generating random numbers in smart contracts is a topic of active research and several techniques exist to do so securely [25, 26], including ones that use an oracle [22]. Finally, the voter submits a sealed vote . This can be accomplished using a commit-reveal scheme in which the voter commits to a hash of their vote concatenated with a nonce and later reveals the vote and nonce. We define an honest voter as one who always votes according to their belief .

Iv-C2 Certifying

Players may place a large deposit in order to certify propositions of their choosing. The certifier simply submits a monetary stake and a sealed certification for proposition . An honest certifier is one who always certifies according to their belief .

Iv-C3 Termination and Decision

Once a proposition has accumulated sufficient voting stake, it is decided. The amount of voting stake before decision is a parameter of the system denoted by . Four values are computed: , , , and . These values represent, respectively, the total voting stake for true, total voting stake for false, total certifying stake for true, and total certifying stake for false. For each , they are computed as follows:

Outcome Condition
TABLE I: Voting outcomes
Outcome Condition
TABLE II: Certifying outcomes

Voting and certifying outcomes are computed as shown in Tables I and II. It can be seen that a simple majority determines the outcome. In case of a tie, the voting outcome is unknown (denoted by Ø). The same formula applies for certification outcomes. Alternatively, the system can require a super-majority instead of a simple majority for a definite and outcome and produce a Ø outcome otherwise. Ultimately this does not affect the design or the analysis of the game and it is excluded from the description for the sake of simplicity.

The game and oracle outcomes that correspond to each of the nine possible combinations of certification and voting results are illustrated in Table III. The headings in the top row correspond to certification, while the labels in the first column correspond to voting.

(a) Game
(b) Oracle
TABLE III: Outcomes for (a) the game and (b) the oracle

The game has three possible outcomes: true (), false (), and unknown (Ø), each of which carries its own reward structure. Note that the game outcome is only used to determine rewards and penalties, and does not necessarily correspond exactly to the oracle’s output. Indeed, anyone observing the system is free to compute oracle outcomes as they wish and depending on the context of the proposition. For the sake of this presentation a suggested mapping is presented in Table III-b. The suggested oracle output follows the voting outcome if it matches the certification outcome or the certification outcome is Ø. The oracle is not restricted to an output of , but could instead have an output in the range indicating confidence in the truth or falsity of the proposition.

Reward Penalty
Outcome Voters Certifiers Voters Certifiers
TABLE IV: Summary of rewards and penalties

Iv-D Rewards and Penalties

Broadly speaking, players are only rewarded for and outcomes in which they took a position that matches it. Conversely, those who took opposing positions are penalized. In unknown outcomes, certifiers are penalized and voters receive no rewards or penalties. As argued in the paper, this scheme incentivizes the participants to behave honestly on the validity of propositions.

For the rest of this subsection, fix a player and proposition to be decided so as to enumerate the rewards and penalties for each of the three possible game outcomes. Voter and certifier rewards are presented separately although, as noted earlier, nothing prohibits a player from being both a voter and a certifier.

Rewards and penalties are distilled into a single value for voting and for certification. A negative value indicates a penalty, while a positive one indicates a reward. The results are summarized in Table IV.

Iv-D1 True and False Outcomes

In the case of a outcome, the voting reward is as follows.


The player’s vote reward is their share of the -voting stake times the proposition’s bounty amount. Their penalty is equal to their -voting stake. The certifier reward is shown in Eq. 3 below.


A certifier’s reward is equal to her share of the -certifying stake times the true certifier reward pool amount times the reciprocal of the certification target . The true reward pool is a reward pool used to reward certifiers who correctly certify articles as true. The certification target can be seen as the number of certifications that the pool should have enough funds to pay for. For instance, if and , then monetary units will be distributed to the certifiers. The next proposition will have , and therefore units will be distributed.

In the case of an outcome, the rewards and penalties are similar.

Iv-D2 Unknown Outcome

For an outcome of Ø (unknown), voters are neither rewarded nor penalized (), while certifiers are penalized as follows.


That is, certifiers forfeit all of their stake, regardless of agreement with voters. The rationale for penalizing certifiers and not voters is that certifiers chose to certify proposition while voters did not choose to vote on it as they received it at random.

Iv-E Monetary Flows

Note that voters are not rewarded for unknown outcomes, and therefore bounties are not claimed. Thus far, the distribution of penalties and unclaimed bounties has not been discussed, and the funding of reward pools and bounty amounts has only been briefly mentioned.

Submitter fees are used to fund bounties, while the certifier reward pools are initially left empty. Certifier reward pools are funded by unclaimed bounties and penalties. In the absence of reward pools, certification will be rare, which will lead to most bounties being unclaimed. It is expected that this method will approach equilibrium where reward pools and bounties are balanced to provide reasonable incentives for both voters and certifiers. Further, it is adaptable as it can approach a new equilibrium automatically if external conditions change.

An additional consideration is the draining of reward pools. Each time a proposition is decided with voting outcome , an amount is subtracted from . If the certification outcome is also , the funds are used to pay out certifier rewards. Otherwise, the funds are added to . A symmetric case applies for false outcomes. The reasoning behind this is explained in Section V-D but its intuition lies in the fact that it ensures that the reward pools encourage certifiers to certify equal numbers of true and false propositions, thereby discouraging voters from voting with constant or values in order to maximize profit without considering the actual propositions.

V System Analysis

To analyze Astraea we first construct formulas relating the parameters of the system to the probability of the voting procedure producing incorrect results (i.e., where the outcome for proposition with truth value is ). Next, we introduce mathematics that relate the system parameters to the minimum accuracy needed by voters so that they remain profitable. Subsequently, we prove that a Nash equilibrium exists where all players play honestly under a form of honest majority assumption on the voters. Finally, we argue that the certifier reward structure avoids a situation where players profitably vote and certify everything with a constant or , even if the proposition list is heavily biased towards true or false propositions.

V-a Voting Outcomes and Manipulation

This subsection determines the probability that voting outcomes are correct as a function of accuracy and extends the analysis to determine an adversary’s probability of forcing incorrect outcomes. For simplicity, we assume all non-adversarial players are honest, have the same accuracy , and always vote with monetary units of stake. We can therefore treat the voting process on a single proposition as a sequence of Bernoulli trials with probability of success. The probability that the voting outcome is correct is therefore:


denotes a binomial random variable. For example, if

, , and , the probability of obtaining a correct voting outcome is roughly %.

Now let us assume an adversary has monetary units and seeks to force an incorrect outcome on a specific proposition. For simplicity, we assume is a multiple of and that the proposition list does not change during the attack. Each proposition can once again be modeled as a sequence of Bernoulli trials. Each trial is successful with probability:

where is the probability that the vote belongs to the adversary.

If the adversary uses all tokens to vote, then votes belong to the adversary across all propositions. Once all propositions in the proposition list are decided, the probability that an arbitrarily-chosen vote belongs to the adversary is:

So the probability that an arbitrary vote is incorrect is:


Note, both and appear in the denominator demonstrating that increasing these parameters renders system manipulation more difficult. The probability of an adversary changing the outcome of a proposition is shown below:

It can be seen that if the quantity in Eq. 5 is less than 0.5, there are parameter values that make it arbitrarily difficult for the adversary to force an incorrect result. Table V shows the adversary’s chance of success for various parameter values. The six columns show the voting stake before decision, the size of the proposition list, the voter accuracy, the fraction of votes controlled by the adversary, the probability of forcing an incorrect output for a specific proposition, and the probability of doing so for any proposition, respectively. The rows where no votes are controlled by an adversary show the probability of an incorrect outcome occurring due to honest voter behavior alone. It can be seen that if voters are 95% accurate and , manipulation is effectively impossible, even by a powerful adversary controlling 25% of the votes.

TABLE V: Probability of Adversary Manipulating Voting

V-B Minimum Voting Accuracy

According to the analysis in the previous subsection, the accuracy of honest voters is critical to the security of Astraea. This subsection quantifies the minimum accuracy (i.e., the probability that the player’s belief matches the truth value of proposition ) players need to achieve profitability in expectation by constructing formulas that relate the accuracy threshold to the parameters of the system. Since making it more difficult to earn a profit is expected to lower participation, it is critical to set the parameters carefully to achieve a reasonable tradeoff between accuracy and participation.

For simplicity, we assume the parameters are set such that the probability of incorrect decisions is negligible. Consider player with accuracy . A vote with stake of on proposition yields a profit in expectation when, at decision time for :


In other words, the expected share of the voting rewards is greater than the expected penalties. Note that there is no need to account for Ø outcomes since voters receive neither rewards nor penalties in that case. At decision time, the denominator is clearly at least half of , and at most . Therefore:


It is clear from Eq. 6 that the voter is profitable for sufficiently high values of . Towards the goal of computing an upper bound, we over-approximate the range in which a voter is profitable using Eq. 7 as follows.

Re-arranging yields the following upper bound on :


By capping the bounty according to Eq. 8, it is possible to enforce a minimum accuracy such that below that threshold voting becomes unprofitable. For instance, if 80% accuracy is desired and , the bounty must be capped at monetary units. If instead 50% accuracy is desired the bounty must be capped at . Of course this analysis only lower-bounds the threshold; it neglects the voter’s costs in terms of time to evaluate propositions, computing power, and blockchain transaction fees.

V-C Desirable Nash Equilibrium

This subsection demonstrates the existence of a desirable Nash equilibrium in which all players are honest. Indeed, it is clear that any situation in which all players always vote and certify in concert is a Nash equilibrium, as any player who votes against all the others will only stand to lose. However, we seek to show that such an equilibrium exists under the assumption that the quantity in Eq. 5 is less than . In effect, this assumes that honest voters are sufficiently accurate and in such plurality that a majority of votes are correct. From the analysis in Section V-B, the assumption is sufficient to show that there exists an assignment to the parameters such that all propositions have the correct voting outcome with overwhelming probability.

While we omit the details of the analysis due to space requirements, it is clear that playing honestly is a Nash equilibrium when every voting outcome is correct and only feasible strategies are considered. Rewards are only ever paid to players who agree with the voting outcome. Since every proposition has the voting outcome , if player votes or certifies (i.e., honestly), she agrees with the voting outcome with probability . Naturally, an honest player could perform better by switching to a “perfect” strategy in which they always vote correctly rather than honestly, but such a strategy is not feasible since players do not know the underlying truth values. Since all beliefs are independent by assumption, a player cannot develop complex strategies that leverage statistical correlation between beliefs to vote correctly with probability better than . Even an adversary with perfect accuracy who controls 100% of the certifying stake is incentivized to play honestly (or not play at all e.g., in the case where and every proposition is true). Indeed, any other strategy results in the adversary losing all of their stake.

V-D Proposition Bias and Reward Pools

While the previous subsection demonstrates that playing honestly is an equilibrium under the assumption that an adversary does not control voting, this assumption may not hold if a dishonest strategy is easier and still profitable. In this subsection, we identify a candidate for such a strategy and argue that the reward structure combats it.

Imagine true propositions are more common than false ones and define as a lazy voter one who always votes . Let denote the probability that a random proposition is true. We further assume as before that all voting outcomes are correct, so the lazy voter agrees with the voting outcome on every true proposition and disagrees on every false proposition. Intuitively, this lazy strategy seems viable, but note that it is also necessary to consider certifier behavior since without certification no rewards are paid out. Certifier incentives are tied to the certifier reward pools, and their values fluctuate over time.

When a true proposition is decided, the pool will shrink by . Over time the pool will drain much faster than the pool when . Indeed, the pool may actually grow in this case.

Again, we omit the details of the formal argument due to space restrictions. However, informally, this process incentivizes certifiers to make more certifications on propositions that they believe are false, since the potential rewards are greater. At equilibrium, roughly equal amounts of true and false propositions should carry certifications, meaning that the lazy strategy will not be profitable. Note that certifiers are never incentivized to certify a true proposition as false in an attempt to acquire the reward, as in that case the certifier will disagree with voters and be penalized.

Vi Extension to Unknown Propositions and Data Availability

This section presents an extension to simultaneously handle two issues that would arise from a practical implementation of Astraea.

  1. A proposition may not have a clear answer between true and false, e.g. if the proposition is “Is complexity class P equal to NP?” [27] Since voters are assigned a proposition randomly, they may be assigned a proposition for which they cannot vote towards the truth value, since the truth for some is unknown.

  2. As storage directly on the blockchain is relatively expensive [28], an implementation of Astraea would most likely use an off-chain storage solution for propositions, allowing them to be uniquely identified by an immutable public hash [29]. As such, the problem of data availability [30] presents itself: what if the submitter does not propagate her proposition sufficiently for the majority of the network to see it, or a malicious actor submits a proposition but intentionally does not share the data corresponding to the hash? Voters would again be unable to vote towards the truth, in this case because the question is unavailable to them.

In both cases, the assumption in Section II-C that each proposition has a truth value is violated. Astraea can be extended by adding a third option for voters, this of unknown. If the voting outcome is unknown (Ø) due to a majority of voters voting unknown, voters are neither rewarded nor punished, as in Section IV-D2. Certifiers may not take a position of unknown, they should simply abstain from participating in such cases. The reward structure for the game outcomes remains the same as described in Section IV, and the analysis of desiderata follows in a straightforward manner from that in Section V. This extension protects players from penalization when submitters provide unclear propositions or withhold data.

Vii Applications

Practical applications of a decentralized, permissionless, and trustless oracle are numerous. This section gives an overview of candidate use cases for Astraea.

Machine Learning and Data Annotation:

Modern data science techniques require a tremendous amount of annotated data 

[31] to train predictive models, with applications ranging from self-driving cars, to targeted marketing or medical diagnoses. Centralized crowd-sourcing platforms [32, 33] offer a means for individuals to perform human intelligence tasks and receive a payment. However, there have been reports of these platforms not compensating workers properly [34] and due to the lack of incentives to label data correctly, low-quality labeling is prevalent in the industry. This requires customers to pay for redundant work, since there is no easy means of actually determining which labels are incorrect. A decentralized oracle that incentivizes workers to vote honestly can be used for data annotation, potentially reducing cost and improving quality over existing solutions.

Data Availability: Decentralized applications that make use of off-chain resources [10] suffer from the data availability problem [30], in which off-chain data may only exist transiently, or may never have existed at all (e.g. in the case of a malicious actor). Astraea, with the extension of Section VI, can be used as a data availability oracle for all such applications.

Adjudication Mechanisms: Negotiations between parties that require an adjudication mechanism can instead use a decentralized oracle such as Astraea. In this case, the oracle will essentially serve as a public jury. Decentralized applications that deal with real-world resources, such as legal agreements, transfers of assets, etc. can make use of this system.

Viii Conclusion

This work introduces a decentralized, trustless, and permissionless blockchain oracle system, Astraea. Submitters enter propositions into the system, while voters and certifiers play a game to determine the truth value of each proposition. We analyze the game-theoretical incentive structure to show that a desirable Nash equilibrium exists whereby under a set of simple assumptions all rational players behave honestly.