Every theory of choice must answer a question that is easy to state and hard to settle. Does the mind evaluate each option on its own and then select the winner? Or does it build preference directly from the differences between options? The first view descends from von Neumann and Morgenstern, for whom choice is the maximization of a scalar utility assigned to each lottery independently. The second has an equally long but less celebrated lineage, running through Tversky's lexicographic semiorders and the regret theory of Loomes and Sugden.

The distinction is more than architectural. Integration models imply that an option's value is fixed before it meets its competitors. That commitment entails transitivity and independence from irrelevant alternatives. Comparison models make no such promise. In them, value is relational and constructed on the fly, so it responds to context in ways integration forbids. Decoy effects, preference reversals, and intransitive cycles are anomalies for one family of models and natural predictions for the other.

Neuroeconomics has sharpened the question rather than resolved it. There is strong evidence for a common currency of value in ventromedial prefrontal cortex. There is equally strong evidence for attribute-wise comparison signals elsewhere in the brain. So the more productive question is not which theory is correct. It is which computational route a given task recruits, and why. This article examines both routes and the conditions under which each better describes behavior.

In the integration framework, each option is mapped to a scalar by a function that ignores the rest of the choice set. Expected utility is the canonical case: a lottery's value is the probability-weighted sum of the utilities of its outcomes. Multi-attribute utility theory extends this logic to riskless goods. It typically assumes additive separability, so a car's value is a weighted sum of the values of its price, reliability, and fuel economy.

Choice then reduces to comparing scalars. In stochastic versions, a Luce or logit rule converts value differences into choice probabilities. Sequential sampling models such as the drift diffusion model accumulate noisy evidence about the difference in integrated values until a threshold is reached. Krajbich and Rangel's attentional drift diffusion model keeps this structure. It adds one twist: visual fixations modulate the rate at which each option's value enters the accumulator.

The neural case for integration is substantial. Padoa-Schioppa and Assad found orbitofrontal neurons in monkeys that encoded the subjective value of offered juices regardless of what they were paired with. They called this property menu invariance. In humans, the fMRI meta-analysis by Bartra, McGuire, and Kable locates a domain-general value signal in ventromedial prefrontal cortex and ventral striatum. That signal responds to money, food, and social rewards alike.

The theoretical appeal is equally clear. Independent valuation guarantees transitivity and satisfies Luce's choice axiom. It is also computationally economical: with n options, a decision maker computes n valuations rather than n(n−1)/2 pairwise comparisons. And a common currency permits comparison of goods that share no attributes at all, such as a concert ticket against a dinner out.

Yet the framework carries a burden of proof that grows heavier with each documented context effect. If an option's value is fixed before it meets its rivals, adding a dominated decoy should never increase the choice share of the option it resembles. It does, robustly, as Huber, Payne, and Puto showed in 1982. Integration models can absorb such findings only by adding normalization or attention mechanisms. Those additions quietly reintroduce comparison through the back door.

Takeaway

Independent valuation buys transitivity, efficiency, and a common currency at the cost of insensitivity to context. Every robust context effect is a debt that integration models must pay with additional machinery.

Comparison models invert the order of operations. Integration aggregates attributes within each option and then compares the totals. Comparison does the reverse: it compares options within each attribute and then aggregates the resulting advantages. Formally, preference for A over B becomes a function of attribute-wise differences, f(a₁ − b₁, a₂ − b₂, …). That function need not decompose into separate valuations of A and B.

Tversky's 1969 work on intransitivity showed the consequences. Under a lexicographic semiorder, small differences on a primary dimension are ignored in favor of a secondary dimension, which yields predictable preference cycles. Regret theory, due to Loomes and Sugden, adds a different relational element. It makes the evaluation of an outcome depend on what the forgone option would have yielded in the same state of the world. This produces transitivity violations that expected utility cannot express.

Contemporary models generalize these ideas. Multialternative decision field theory, developed by Roe, Busemeyer, and Townsend, lets attention switch stochastically between attributes while options compete against one another. A single architecture reproduces similarity, attraction, and compromise effects. In risky choice, the priority heuristic compares gambles reason by reason, and salience theory weights states by how sharply payoffs contrast across options. In intertemporal choice, Ericson and colleagues found that an attribute-wise model predicted out-of-sample choices better than standard discounting models.

Process data support the account. Eye-tracking studies routinely show gaze moving between options on the same attribute, which is the signature of within-attribute comparison. Noguchi and Stewart found that such transitions dominate in tasks that produce context effects. Neurally, Hunt, Dolan, and Behrens reported attribute-level comparison signals in intraparietal sulcus. These signals were anatomically separable from the integrated value comparison in ventromedial prefrontal cortex.

The cost of comparison is coherence. Relational evaluation sacrifices transitivity and the guarantee of a stable ordering, and it struggles with options that share few comparable attributes. But comparison economizes on a different resource. It avoids the need to estimate absolute attribute weights, substituting the cheaper and more reliable judgment of which option is better on a given dimension. Psychophysics has long shown that relative judgments are more accurate than absolute ones, and comparison models extend that principle to value.

Takeaway

Comparison models treat preference as a relation between options rather than a property of each one. They trade the guarantee of coherence for the reliability of relative judgment.

If both routes exist, the theoretical problem becomes one of strategy selection. Payne, Bettman, and Johnson's adaptive decision maker framework anticipated this. In their account, decision makers trade accuracy against effort and shift between compensatory and noncompensatory strategies as task demands change. The modern version of the question is sharper: which structural features of a choice favor integration, and which favor comparison?

Attribute alignment is the first feature. When options share aligned dimensions, such as two apartments differing in rent and commute time, attribute-wise comparison is natural and cheap. When options are nonaligned, such as a vacation versus a home repair, there is nothing to compare dimension by dimension. The decision maker must retreat to abstract, integrated evaluation. Johnson's research on noncomparable alternatives documented exactly this shift toward holistic representations.

Presentation format is the second. Showing options simultaneously in an attribute matrix promotes attribute-wise search. Sequential presentation forces each option to be encoded before its rival appears, which favors independent valuation. Hsee's distinction between joint and separate evaluation captures the behavioral consequence. Attributes that are hard to evaluate in isolation gain weight under joint evaluation, producing preference reversals across modes.

Complexity and set size form the third axis. Arieli, Ben-Ami, and Rubinstein found that eye movements in risky choice followed holistic patterns when gambles were easy to evaluate. When probabilities and outcomes became harder to combine, gaze shifted toward dimension-wise comparison. Set size pushes in the other direction. Pairwise comparisons grow quadratically with the number of options, so large sets tend to be screened into a small consideration set first. That two-stage pattern is well documented in consumer choice.

Learning history matters as well. Options experienced repeatedly acquire cached values, the reinforcement-learning analogue of integration, and can be retrieved without deliberation. Novel options described by their attributes must be constructed on the spot, and construction tends to be comparative. This suggests a developmental arc: comparison may scaffold the formation of values that later behave as though they had been integrated all along.

Takeaway

Instead of asking whether people integrate or compare, ask what the task makes cheap. Aligned attributes, simultaneous display, complexity, and novelty favor comparison, while familiarity and incommensurable options favor integration.

The contrast between integration and comparison is best understood not as a contest between rival theories. It is a map of the computational options available to a resource-constrained system. Each route leaves a characteristic signature. Integration predicts menu invariance and transitivity, while comparison predicts context dependence and occasional cycles.

This reframing has methodological consequences. Testing a choice model on a single task format risks mistaking a task-induced strategy for a general law of preference. Process tracing, neural recording, and deliberate manipulation of attribute alignment and presentation format should be standard instruments, not supplements.

It also unsettles von Neumann's elegant premise. If value is sometimes a property and sometimes a relation, utility is less a fixed quantity than a product of how the choice is posed. The question of what a person prefers then cannot be separated from the question of how they were asked.