Abstract: Considering information cascades (both upwards and downwards) as a problem of incentives, better incentive design holds some promise. This academic paper suggests a model in which making truth-finding rewards contingent on reaching a certain number of votes prevents down-cascades, and where an informed (self-interested) choice of payout odds and threshold can also prevent up-cascades in the limit of a large population of predictors.
1)cf.avturchin from the question about distribution across fields, pointing out that up-cascades and down-cascades are both relevant concerns, in many contexts.
2) Consider information cascades as related to a problem of incentives—in the comments of the Johnichols post referenced in the formalization question, multiple commentators point out that the model fails if agents seek to express their marginal opinion, rather than their true (posterior) belief. But incentives to be right do need to be built into a system that you’re trying to pump energy into, so the question remains of whether a different incentive structure could do better, while still encouraging truth-finding.
3)Up-Cascaded Wisdom of the Crowd (Cong and Xiao, working paper) considers the information-aggregation problem in terms of incentives, and consider the incentives at play in an all-or-nothing crowdfunding model, like venture capital or Kickstarter (assuming that a ‘no’ vote is irrevocable like a ‘yes’ vote is) -- ‘yes’ voters win if there is a critical mass of other ‘yes’ voters and the proposition resolves to ‘yes’; they lose if there is a critical mass and the proposition resolves to ‘no’; they have 0 loss/gain if ‘yes’ doesn’t reach a critical mass; ‘no’ voters are merely abstaining from voting ‘yes’.
Their main result is that if the payment of incentives is conditioned on the proposition gaining a fixed number of ‘yes’ votes, a population of symmetric, common-prior/private-info agents will avoid down-cascades, as a single ‘yes’ vote that breaks a down-cascade will not be penalized for being wrong unless some later agent intentionally votes ‘yes’ to put the vote over the ‘yes’ threshold. (An agent i with negative private info still should vote no, because if a later agent i’ puts the vote over the ‘yes’ threshold based in part on i’s false vote, then i expects to lose on the truth-evaluation, since they’ve backed ‘yes’ but believe ‘no’.)
A further result from the same paper is that if the actor posing the proposition can set the payout odds and the threshold in response to the common prior and known info-distribution, then a proposition-poser attempting to minimize down-cascades (perhaps because they will cast the first ‘yes’ vote, and so can only hope to win if the vote resolves to ‘yes’) will be incentivized to set odds and a threshold that coincidentally minimize the chance of up-cascades. In the large-population limit, the number of cascades under such an incentive design goes to 0.
4) I suspect (but will not here prove) that augmenting Cong and Xiao’s all-or-nothing “crowdfunding for ‘yes’” design with a parallel “crowdfunding for ‘no’” design—i.e., ‘no’ voters win (resp. lose) iff there is a critical mass of ‘no’ voters and the proposition resolves ‘no’ (resp. ‘yes’) -- can further strengthen the defenses against up-cascades (by making it possible to cast a more informed ‘no’ vote conditioned on a later, more-informed agent deciding to put ‘no’ over the threshold).
A related idea in non-punishment of “wrong” reports that have insufficient support (again in the common-prior/private-info setting) comes from this paper [pdf] (presented at the same conference), which suggests collecting reports from all agents and assigning rewards/punishments by assuming that agents’ reports represent their private signal, computing their posterior, and scoring this assumed posterior. Under the model assumptions, this makes it an optimal strategy for agents to truly reveal their private signal to the mechanism, while allowing the mechanism to collect non-cascaded base data to make a decision.
In general, I feel like the academic literature on market design / mechanism design has a lot to say about questions of this flavor.
A further result from the same paper is that if the actor posing the proposition can set the payout odds and the threshold in response to the common prior and known info-distribution, …
This is a really cool result, but I’m confused about why it holds. Is the idea something like: the actor themself is uncertain about the value of the project, and the kickstarter also helps them find out whether it’s worth doing, so up-cascades are costly in expectation (they might land themselves having to run some awful project)?
But if is the mechanism, it seems to apply to any rational actor using a kickstarter, as opposed to having anything to do with minimizing down-cascades?
Is the idea something like: the actor themself is uncertain about the value of the project, and the kickstarter also helps them find out whether it’s worth doing
Nope! The paper’s model for this result assumes that the value conditioned on success is known to the proposer, so that the proposer’s only incentive is to maximize their own profits by setting the payout odds and threshold. The (non-obvious to me) result that the paper proves is that this coincidentally minimizes the probability of up-cascades:
A higher decision threshold excludes more DOWN cascades while it is less likely to be reached. We show that the concern about potential DOWN cascades dominates the concern about likelihood to reach the target. To maximize the proceeds, the proponent endogenously sets the target to the smallest number that in equilibrium completely excludes DOWN cascades in the same spirit as Welch (1992), with the caveat that the proponent utilizes both price and target to achieve this. Consequently, with endogenous issuance pricing, there is no DOWN cascade which stops private information aggregation, and good projects are always financed while bad projects are never financed, when the crowd base N becomes very large. In other words, financing efficiency and information aggregation efficiency approaches the first best as N grows bigger, despite the presence of information cascades.
It references existing (and novel) work in economics and mechanism design, which might have been time-consuming to discover otherwise
It distills a technical paper, which is a valuable service that is usually underfunded (academic institutions comparatively incentivise novel and surprising insights)
The insights provided are quite action-guiding, and caused me (jacobjacob) to have ideas for how one can experiment with new kinds of forecasting tournaments that use a threshold-mechanism to change participant incentives
Abstract: Considering information cascades (both upwards and downwards) as a problem of incentives, better incentive design holds some promise. This academic paper suggests a model in which making truth-finding rewards contingent on reaching a certain number of votes prevents down-cascades, and where an informed (self-interested) choice of payout odds and threshold can also prevent up-cascades in the limit of a large population of predictors.
1) cf. avturchin from the question about distribution across fields, pointing out that up-cascades and down-cascades are both relevant concerns, in many contexts.
2) Consider information cascades as related to a problem of incentives—in the comments of the Johnichols post referenced in the formalization question, multiple commentators point out that the model fails if agents seek to express their marginal opinion, rather than their true (posterior) belief. But incentives to be right do need to be built into a system that you’re trying to pump energy into, so the question remains of whether a different incentive structure could do better, while still encouraging truth-finding.
3) Up-Cascaded Wisdom of the Crowd (Cong and Xiao, working paper) considers the information-aggregation problem in terms of incentives, and consider the incentives at play in an all-or-nothing crowdfunding model, like venture capital or Kickstarter (assuming that a ‘no’ vote is irrevocable like a ‘yes’ vote is) -- ‘yes’ voters win if there is a critical mass of other ‘yes’ voters and the proposition resolves to ‘yes’; they lose if there is a critical mass and the proposition resolves to ‘no’; they have 0 loss/gain if ‘yes’ doesn’t reach a critical mass; ‘no’ voters are merely abstaining from voting ‘yes’.
Their main result is that if the payment of incentives is conditioned on the proposition gaining a fixed number of ‘yes’ votes, a population of symmetric, common-prior/private-info agents will avoid down-cascades, as a single ‘yes’ vote that breaks a down-cascade will not be penalized for being wrong unless some later agent intentionally votes ‘yes’ to put the vote over the ‘yes’ threshold. (An agent i with negative private info still should vote no, because if a later agent i’ puts the vote over the ‘yes’ threshold based in part on i’s false vote, then i expects to lose on the truth-evaluation, since they’ve backed ‘yes’ but believe ‘no’.)
A further result from the same paper is that if the actor posing the proposition can set the payout odds and the threshold in response to the common prior and known info-distribution, then a proposition-poser attempting to minimize down-cascades (perhaps because they will cast the first ‘yes’ vote, and so can only hope to win if the vote resolves to ‘yes’) will be incentivized to set odds and a threshold that coincidentally minimize the chance of up-cascades. In the large-population limit, the number of cascades under such an incentive design goes to 0.
4) I suspect (but will not here prove) that augmenting Cong and Xiao’s all-or-nothing “crowdfunding for ‘yes’” design with a parallel “crowdfunding for ‘no’” design—i.e., ‘no’ voters win (resp. lose) iff there is a critical mass of ‘no’ voters and the proposition resolves ‘no’ (resp. ‘yes’) -- can further strengthen the defenses against up-cascades (by making it possible to cast a more informed ‘no’ vote conditioned on a later, more-informed agent deciding to put ‘no’ over the threshold).
A related idea in non-punishment of “wrong” reports that have insufficient support (again in the common-prior/private-info setting) comes from this paper [pdf] (presented at the same conference), which suggests collecting reports from all agents and assigning rewards/punishments by assuming that agents’ reports represent their private signal, computing their posterior, and scoring this assumed posterior. Under the model assumptions, this makes it an optimal strategy for agents to truly reveal their private signal to the mechanism, while allowing the mechanism to collect non-cascaded base data to make a decision.
In general, I feel like the academic literature on market design / mechanism design has a lot to say about questions of this flavor.
This is a really cool result, but I’m confused about why it holds. Is the idea something like: the actor themself is uncertain about the value of the project, and the kickstarter also helps them find out whether it’s worth doing, so up-cascades are costly in expectation (they might land themselves having to run some awful project)?
But if is the mechanism, it seems to apply to any rational actor using a kickstarter, as opposed to having anything to do with minimizing down-cascades?
Nope! The paper’s model for this result assumes that the value conditioned on success is known to the proposer, so that the proposer’s only incentive is to maximize their own profits by setting the payout odds and threshold. The (non-obvious to me) result that the paper proves is that this coincidentally minimizes the probability of up-cascades:
We (jacobjacob and Ben Pace) decided to award $250 (out of the total bounty of $800) to this answer. It does several important things.
It references existing (and novel) work in economics and mechanism design, which might have been time-consuming to discover otherwise
It distills a technical paper, which is a valuable service that is usually underfunded (academic institutions comparatively incentivise novel and surprising insights)
The insights provided are quite action-guiding, and caused me (jacobjacob) to have ideas for how one can experiment with new kinds of forecasting tournaments that use a threshold-mechanism to change participant incentives
I’ll PM you for details about payment.