Large language models (LLMs) are increasingly used as synthetic personas representing survey respondents. Their validity as substitutes for particular respondents depends on whether they reproduce individuals' decisions. We examine what information helps synthetic respondents predict each individual's later choices, using five conditions that add progressively richer information: no personal information, demographics, personality traits, cognitive scores, and finally the respondent's earlier survey choices as behavioral history. We use a two-wave panel of 845 US adults who completed measures of 14 behavioral biases (spanning risk, time preferences, overconfidence, and reasoning), so each respondent's earlier answers provide a human test-retest benchmark; in the behavioral-history condition, all items that score the target bias are withheld. At the population level, the average number of biases per respondent in every condition is close to the human average (7.1-8.1 biases, against 7.1 for humans). This aggregate similarity masks differences in variance: persona descriptions recover only 53-67% of human between-person variation, whereas adding behavioral history restores it to approximately the human level. At the individual level, description-based personas achieve only 7-12% of the informedness observed in human test-retest responses, while adding behavioral history raises this to 28%. The condition including behavioral history has the highest estimated informedness in all 17 demographic groups, whereas description-based conditions provide little or no information for some groups. Synthetic responses also exhibit stronger education- and income-related differences than human responses. For LLM synthetic personas, a respondent's past answers add more to individual-level prediction than a description of who they are.

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