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Equation 18 · Part 8 · Why Cost and Latency Belong in the Evaluation Score, Not a Footnote

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Uλ(A)=sA−λc cA−λl lA.U_{\lambda}(A) = s_A - \lambda_c\, c_A - \lambda_l\, l_A .
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What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

Make that judgment explicit and it becomes a scalarized score. Choose exchange rates λc\lambda_c (accuracy points per dollar) and λl\lambda_l (accuracy points per second of latency), and define Uλ(A)=sA−λc cA−λl lAU_{\lambda}(A) = s_A - \lambda_c\, c_A - \lambda_l\, l_A . This is a legitimate way to rank agents, and it is what most procurement decisions ultimately have to do. But writing it out this explicitly makes the hidden step visible: the ranking that comes out depends entirely on λc\lambda_c and λl\lambda_l , numbers that are not properties of the agents at all. A call center with razor-thin per-ticket margins and a research lab doing one-off due-diligence work on a handful of contracts will set λc\lambda_c at wildly different values, and the two will…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.