Name
Abstract | ||
|---|---|---|
Suppose we have a pair of information channels, kappa(1), kappa(2), with a common input. The Blackwell order is a partial order over channels that compares kappa(1) and kappa(2) by the maximal expected utility an agent can obtain when decisions are based on the channel outputs. Equivalently, kappa(1) is said to be Blackwell-inferior to kappa(2) if and only if kappa(1) can be constructed by garbling the output of kappa(2). A related partial order stipulates that kappa(2) is more capable than kappa(1) if the mutual information between the input and output is larger for kappa(2) than for kappa(1) for any distribution over inputs. A Blackwell-inferior channel is necessarily less capable. However, examples are known where kappa(1) is less capable than kappa(2) but not Blackwell-inferior. We show that this may even happen when kappa(1) is constructed by coarse-graining the inputs of kappa(2). Such a coarse-graining is a special kind of " pre-garbling" of the channel inputs. This example directly establishes that the expected value of the shared utility function for the coarse-grained channel is larger than it is for the non-coarse-grained channel. This contradicts the intuition that coarse-graining can only destroy information and lead to inferior channels. We also discuss our results in the context of information decompositions. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.3390/e19100527 | ENTROPY |
Keywords | DocType | Volume |
Channel preorders,Blackwell order,degradation order,garbling,more capable,coarse-graining,62C05,62B15,94A15 | Journal | 19 |
Issue | ISSN | Citations |
10 | 1099-4300 | 2 |
PageRank | References | Authors |
0.37 | 2 | 6 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Johannes Rauh | 1 | 152 | 16.63 |
| Pradeep Kr. Banerjee | 2 | 15 | 1.79 |
| Eckehard Olbrich | 3 | 135 | 16.51 |
| Jost Jürgen | 4 | 71 | 14.59 |
| Nils Bertschinger | 5 | 225 | 21.10 |
| David H. Wolpert | 6 | 4334 | 591.07 |