Reading between the lines and presuming that you reference a local government entity such as a city, county, special district, etc., here's an answer limited only by the information you provide. While the California Public Contracts Code requires government selection of the lowest responsive and responsible bid for public works contracts, you're referencing pre-qualification. That suggests that the bid process in this instance may be informal (forced accounting, under $125K job), is taking place in a charter city with an applicable charter provision, or is not for a public works contract.
Your reference to department head discretion and your allegation of potential fraud suggests that a bit of investigation, analysis and potential action on your part may be warranted. As a former deputy DA specializing in white collar cases and former city attorney, I feel qualified to offer you that comment, even on limited information such as that provided. The pattern of conduct and allegations that you provide suggests that this is far from your first rodeo. Please review my website, and if you think I can help you, feel free to call or email. Good luck.
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