 We then establish that, in the absence of rankings, finding a leximin optimal stable matching is NP-Hard, even under isometric utilities .
<meaning-changed>  We then establish that, in the absence of rankings, finding a leximin optimal stable matching is NP-Hard, even under isometric utilities .
 We then establish that, in the absence of rankings, finding a leximin optimal stable matching is NP-Hard, even under isometric valuations .