Multi-agent LLM systems increasingly let one agent choose which other agents to work with, and agents are increasingly given personalities through personas. We test whether Big Five personality alone influences partner selection when capability is explicitly held constant. Host agents chose among six validated candidate archetypes -- five marked high on one trait (openness, conscientiousness, extraversion, agreeableness, neuroticism) plus a balanced control -- presented with randomized names and ordering across five task categories (375 trials). With neutral hosts (Study 1, n=150), selection departed drastically from chance ($χ^2(5)=325.8$, $p<.001$), following a task-stereotype map: the open archetype won 100% of creative trials, the conscientious archetype 90-97% of strategic, synthesis, and problem-solving trials, and the neurotic archetype 37% of analytical trials (Cramer's V=.74); the extraverted, agreeable, and balanced archetypes were almost never chosen, although human meta-analyses identify team agreeableness as among the strongest personality predictors of team performance. With personality-assigned hosts (Study 2, n=225), and contrary to human similarity-attraction, self-similar partners were selected below chance (11.1% vs. 16.7%, p=.025) and at greater-than-chance trait distance (p<.0001); conscientious hosts diversified away from their own archetype, recruiting vigilant and open partners. Personality-based selection in LLM agents is real, strong, task-stereotyped, non-homophilous, and miscalibrated against human team-performance evidence -- with direct implications for bias auditing in agent marketplaces.

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