Standard economic theory assumes preferences are stable. You choose what you want, and what you want is revealed by your choices. But this elegant simplicity struggles with a common phenomenon: you might prefer having fewer options.

Consider someone who joins a gym with no candy machines. Or opens a savings account with withdrawal penalties. Or asks a friend to hide their phone during work hours. These behaviors suggest that people value constraints—not because they're irrational, but because they understand something about themselves. They know temptation will arise, and they want protection from their future selves.

Faruk Gul and Wolfgang Pesendorfer developed an axiomatic framework that incorporates this insight into rational choice theory. Their approach doesn't abandon the tools of mathematical economics. Instead, it extends them to accommodate preferences over sets of options—what they call menus—rather than just preferences over individual choices. This seemingly technical shift allows us to formally distinguish between what agents want and what agents are tempted by, enabling welfare analysis that standard revealed preference approaches cannot support.

The Gul-Pesendorfer framework begins with a deceptively simple observation: how you rank a set of options can depend on options you'll never actually choose. This contradicts a standard axiom in choice theory—that only the best available option matters for ranking menus.

Consider two menus. Menu A contains only a healthy salad. Menu B contains both the salad and a rich chocolate cake. Standard theory says if you'll choose salad from both menus, you should be indifferent between them. The cake is irrelevant if you won't select it.

But many people strictly prefer Menu A. Not because they'd choose differently from Menu B—they'd still pick the salad. Rather, they prefer A because the cake's presence creates a cost. Resisting temptation requires effort. The willpower expended diminishes the value of the chosen option.

The Set Betweenness axiom captures this formally. It states that if you prefer menu X to menu Y, then adding Y's options to X shouldn't make things better than X alone. Similarly, it shouldn't make things worse than Y alone. The combined menu falls somewhere between the two extremes. This axiom, combined with standard rationality requirements, characterizes agents who experience temptation but exercise self-control.

Crucially, the framework distinguishes three types of agents. Those with no temptation problems satisfy the Independence axiom—menu ranking depends only on the best element. Those who always succumb to temptation have preferences that reduce to the standard model but with different underlying utility. Those who experience temptation but exercise costly self-control satisfy Set Betweenness without Independence. This third category represents the novel contribution.

Takeaway

When adding options to a choice set makes you worse off—even options you won't choose—you've revealed something about temptation that standard models cannot capture.

The Gul-Pesendorfer representation theorem provides mathematical structure to temptation and self-control. An agent's preferences over menus can be represented by two utility functions: a commitment utility u and a temptation utility v.

The commitment utility u represents what the agent wants from an ex-ante perspective—their considered preferences, what they'd choose with unlimited willpower. The temptation utility v represents what attracts them in the moment of choice—the pull of immediate gratification, hedonic appeal, or visceral desires.

When evaluating a menu, the agent anticipates choosing the option that maximizes u + v. But the menu's value isn't simply this maximum. It's reduced by max v—the temptation cost of the most tempting foregone alternative. Formally: W(A) = max(u(x) + v(x)) - max v(y) where the first maximum is over chosen options and the second over all menu options.

This representation has profound implications. Self-control has a utility cost equal to the temptation value of the most appealing unchosen option. Exercising restraint isn't free—it depletes something, whether we call it willpower, cognitive resources, or psychological energy. The model makes this cost measurable.

The framework also clarifies when commitment has value. An agent benefits from removing tempting options precisely when v(tempting option) exceeds v(option they'd choose). The improvement from commitment equals this difference. This provides a rigorous foundation for evaluating commitment devices, paternalistic policies, and institutional designs that limit choice sets.

Takeaway

Self-control isn't just about what you choose—it's about what you resist. The most tempting option you don't choose still extracts a cost from your decision.

The Gul-Pesendorfer framework transforms how we evaluate policies that restrict choice. Standard welfare economics hesitates to endorse limiting options—more choice weakly dominates less choice under traditional assumptions. But if temptation exists, restriction can improve welfare even by the agent's own standards.

Consider retirement savings. Without commitment, someone might undersave—the temptation utility of current consumption exceeds that of saving, even though commitment utility favors retirement security. Automatic enrollment with opt-out provisions, or penalties for early withdrawal, can improve welfare precisely because they reduce the self-control costs the agent would otherwise bear.

The framework enables quantitative analysis. We can estimate the willingness to pay for commitment devices by observing menu choices. If someone accepts a lower interest rate to lock funds away, the foregone return provides a lower bound on their self-control costs. Laboratory experiments have measured such costs directly, finding substantial magnitudes in domains from food choice to financial decisions.

Policy applications extend beyond individual choice architecture. The framework addresses addiction, where temptation utility might be physiologically amplified. It informs debt contract regulation, where sophisticated lenders might exploit consumers' self-control failures. It guides analysis of default rules, opt-in versus opt-out structures, and cooling-off periods.

Critically, welfare judgments use the commitment utility u, not realized choices. This provides normative grounding that behavioral economics sometimes lacks. We're not imposing external preferences on agents—we're helping them achieve what they themselves prefer when considering options from a position of reflection rather than temptation. The paternalism is libertarian in spirit: expanding options by adding commitment possibilities that agents value.

Takeaway

When people will pay to have options removed, welfare analysis must distinguish between what choices reveal and what agents actually want. Commitment utility provides that foundation.

The Gul-Pesendorfer framework accomplishes something rare in economic theory: it extends the mathematical toolkit without abandoning its foundations. Preferences remain complete and transitive. Agents optimize. But the domain of optimization expands to include menus, and this expansion accommodates a vast range of behaviors that standard theory must label as anomalies.

For behavioral researchers and policy designers, the framework offers both precision and practical guidance. Self-control costs become measurable. Commitment device valuation becomes tractable. Welfare analysis can distinguish temptation from preference change.

Perhaps most importantly, the approach respects agents' own judgments about their well-being. It doesn't require external authorities to determine what people should want. It uses people's preferences over choice sets—including their preference for constraint—to reveal the temptations they struggle against and the commitments they value.