behavioralEconomicsCert
plain-language theorem explainer
behavioralEconomicsCert assembles the certificate that five standard behavioral findings arise in Recognition Science when the configuration dimension is five. Economists modeling agents via the J-cost function would cite this to link loss aversion and related biases to the phi-ladder. The definition is a direct record construction that imports the cardinality proof and the J-cost evaluations for rational and biased agents.
Claim. The behavioral economics certificate is the structure satisfying: the cardinality of BehavioralFinding equals 5, $Jcost(1)=0$, and $Jcost(r)>0$ for all $r>0$ with $r≠1$.
background
Recognition Science models economic behavior through the J-cost function, where Jcost(r) quantifies recognition error for a ratio r. The module defines BehavioralFinding as an inductive type enumerating five canonical biases. The BehavioralEconomicsCert structure requires that the cardinality of this type equals five, that Jcost evaluates to zero at the rational point r=1, and that it is strictly positive for all other positive r. This definition sits in the Economics.BehavioralEconomicsFromRS module, which derives behavioral economics directly from the Recognition Composition Law and the phi-ladder. Upstream, behavioralFindingCount proves the cardinality by decidable enumeration, while rational_agent and biased_agent establish the J-cost properties using Jcost_unit0 and Jcost_pos_of_ne_one.
proof idea
The definition constructs the BehavioralEconomicsCert instance by directly assigning the five_findings field to behavioralFindingCount, the rational field to rational_agent, and the biased field to biased_agent. No additional tactics are required beyond the record syntax.
why it matters
This definition completes the formalization of behavioral economics within Recognition Science by certifying that exactly five findings fit the five-dimensional configuration space. It connects to the broader framework where rational agents correspond to J=0 and biases to J>0, with loss aversion derived as approximately phi squared. As the terminal definition in the module, it provides the interface for downstream economic models, though no further uses are recorded yet. It touches the open question of deriving specific bias magnitudes from the phi-ladder without additional parameters.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.