| Summary: | <p>According to critical-level views in population axiology, an extra life improves a population if and only if that life’s welfare level exceeds some fixed “critical level.” An extra life at the critical level leaves the new population equally good as the original. According to critical-range views, an extra life improves a population if and only if that life’s welfare level exceeds some fixed “critical range.” An extra life within the critical range leaves the new population incommensurable with the original.</p>
<p>In this paper, I sharpen some old objections to these views and offer some new ones. Critical-level views cannot avoid certain repugnant and sadistic conclusions. Critical-range views imply that lives featuring no good or bad components whatsoever can nevertheless swallow up and neutralize goodness and badness. Both classes of view imply discontinuities in implausible places. I then offer a view that retains much of the appeal of critical-level and critical-range views while avoiding the above pitfalls. On the Imprecise Exchange Rates View, various exchange rates—between pairs of goods, between pairs of bads, and between goods and bads—are imprecise. This imprecision is the source of incommensurability between lives and between populations.</p>
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