Usually the market have rules that define the bet more concretely than just "there will be a ceasefire", and resolutions can be disputed where they will be arbitrated by the market operator. For this particular market you can see that here (https://polymarket.com/event/us-x-iran-ceasefire-by), but I'll paste the current text too:

    This market will resolve to “Yes” if there is an official ceasefire agreement, defined as a publicly announced and mutually agreed halt in direct military engagement, between the United States and Iran by the listed date, 11:59 PM ET.

    For the purposes of this market, an “official ceasefire agreement” requires clear public confirmation from both the United States government and the government of Iran that they have agreed to halt military hostilities against one another, or for an official ceasefire agreement to be otherwise confirmed to have been reached by an overwhelming consensus of media reporting.

    If the agreement is officially reached before the resolution date, this market will resolve to “Yes,” regardless of whether the ceasefire officially takes effect after the resolution date.

    Any form of informal understanding, backchannel communication, de-escalation without an announced agreement, or unilateral pause in hostilities will not be considered an official ceasefire. Humanitarian pauses, limited operational pauses, or temporary tactical stand-downs will not count toward the resolution of this market.

    A broader peace deal, normalization agreement, or political framework will qualify only if it includes a publicly announced and mutually agreed halt in military engagement between the United States and Iran, effective on a specified date, or otherwise confirmed by an overwhelming consensus of credible reporting. Agreements that outline future negotiations or de-escalation measures without an explicit, dated commitment to stop fighting will not qualify.

    This market’s resolution will be based on official statements from the United States government and the government of Iran. However, an overwhelming consensus of credible media reporting confirming that an official ceasefire agreement has been reached will suffice.

So the real answer is, "whoever the market operator chooses".