License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2018.164
URN: urn:nbn:de:0030-drops-91682
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Ben-Sasson, Eli ; Saig, Eden

Brief Announcement: Towards an Abstract Model of User Retention Dynamics

LIPIcs-ICALP-2018-164.pdf (0.2 MB)


A theoretical model is suggested for abstracting the interaction between an expert system and its users, with a focus on reputation and incentive compatibility. The model assumes users interact with the system while keeping in mind a single "retention parameter" that measures the strength of their belief in its predictive power, and the system's objective is to reinforce and maximize this parameter through "informative" and "correct" predictions.
We define a natural class of retentive scoring rules to model the way users update their retention parameter and thus evaluate the experts they interact with. Assuming agents in the model have an incentive to report their true belief, these rules are shown to be tightly connected to truth-eliciting "proper scoring rules" studied in Decision Theory.
The difference between users and experts is modeled by imposing different limits on their predictive abilities, characterized by a parameter called memory span. We prove the monotonicity theorem ("more knowledge is better"), which shows that experts with larger memory span retain better in expectation.
Finally, we focus on the intrinsic properties of phenomena that are amenable to collaborative discovery with a an expert system. Assuming user types (or "identities") are sampled from a distribution D, the retention complexity of D is the minimal initial retention value (or "strength of faith") that a user must have before approaching the expert, in order for the expert to retain that user throughout the collaborative discovery, during which the user "discovers" his true "identity". We then take a first step towards relating retention complexity to other established computational complexity measures by studying retention dynamics when D is a uniform distribution over a linear space.

BibTeX - Entry

  author =	{Eli Ben-Sasson and Eden Saig},
  title =	{{Brief Announcement: Towards an Abstract Model of User Retention Dynamics}},
  booktitle =	{45th International Colloquium on Automata, Languages, and  Programming (ICALP 2018)},
  pages =	{164:1--164:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Ioannis Chatzigiannakis and Christos Kaklamanis and D{\'a}niel Marx and Donald Sannella},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-91682},
  doi =		{10.4230/LIPIcs.ICALP.2018.164},
  annote =	{Keywords: information elicitation, proper scoring rules, retention complexity}

Keywords: information elicitation, proper scoring rules, retention complexity
Collection: 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)
Issue Date: 2018
Date of publication: 04.07.2018

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