Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Peer Expectation in Robust Forecast Aggregation: The Possibility/Impossibility

Yuqing Kong

Abstract

Recently a growing literature study a new forecast aggregation setting where each forecaster is additionally asked ``what's your expectation for the average of other forecasters' forecasts?''. However, most theoretic results in this setting focus on the scenarios where the additional second-order information helps optimally aggregate the forecasts. Here we adopt an adversarial approach and follow the robust forecast aggregation framework proposed by Arielia, Babichenkoa, and Smorodinsky 2018. We delicately analyze the possibility/impossibility of the new setting when there are two forecasters that either are refinement-ordered or receive conditionally independent and identically distributed (c.i.i.d.) signals. We also extend the setting to a higher level of expectation setting where we can additionally ask ``what's your expectation for the other forecaster's expectation for ...''. The results show that in the above settings, the additional second-order information can significantly improve the aggregation accuracy, and the higher the order, the higher the improvement.

Peer Expectation in Robust Forecast Aggregation: The Possibility/Impossibility

Abstract

Recently a growing literature study a new forecast aggregation setting where each forecaster is additionally asked ``what's your expectation for the average of other forecasters' forecasts?''. However, most theoretic results in this setting focus on the scenarios where the additional second-order information helps optimally aggregate the forecasts. Here we adopt an adversarial approach and follow the robust forecast aggregation framework proposed by Arielia, Babichenkoa, and Smorodinsky 2018. We delicately analyze the possibility/impossibility of the new setting when there are two forecasters that either are refinement-ordered or receive conditionally independent and identically distributed (c.i.i.d.) signals. We also extend the setting to a higher level of expectation setting where we can additionally ask ``what's your expectation for the other forecaster's expectation for ...''. The results show that in the above settings, the additional second-order information can significantly improve the aggregation accuracy, and the higher the order, the higher the improvement.
Paper Structure (61 sections, 15 theorems, 48 equations, 1 figure, 3 tables)

This paper contains 61 sections, 15 theorems, 48 equations, 1 figure, 3 tables.

Table of Contents

  1. Introduction
  2. Summary of Results & Techniques
  3. Expectation Hierarchy
  4. Refinement-ordered
  5. Conditionally Independent
  6. Conditionally Independent Conditioning on a Shared Signal
  7. Many C.I.I.D.
  8. Higher Levels
  9. Insights Behind the Aggregators
  10. Main Techniques
  11. Related Work
  12. One-shot Robust Forecast Aggregation
  13. One-shot Information Aggregation with Second Order Belief
  14. Higher Order Belief
  15. Prior-Independent Mechanism Design & Implementation Theory
  16. ...and 46 more sections

Key Result

Proposition 3.2.0.2.1

When $S_1$ and $S_2$ are independent conditioning on $W$, given any aggregator $a$, for all $Q$ over $\Sigma^2\times\{0,1\}$, there exists a prior $Q'$The prior $Q'$ can depend on the aggregator $a$ and the prior $Q$. over $\{A,B,C\}^2\times\{0,1\}$ such that $\mathbb{E}_Q((a(f_1,f_2,p_1,p_2)-f^*)^2

Figures (1)

  • Figure 1: Higher Level of Expectations

Theorems & Definitions (47)

  • proof : Proof of \ref{['obs:blackwell']}
  • Definition 3.1.0.1.1: $W$'s perspective $o_i,z_i$
  • Definition 3.2.0.1.1: Average Expectation Aggregator
  • Proposition 3.2.0.2.1
  • Corollary 3.2.0.2.2
  • proof : Proof of \ref{['lem:basis']}
  • Claim 3.2.0.3.0
  • Claim 3.2.0.3.0
  • Claim 3.3.0.1.0
  • Definition 3.3.0.1.1: C.I.I.D. Aggregator
  • ...and 37 more