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Automatically increase priority as due date approaches

Thanks for the fantastic productivity tool, first of all. Far and away the best to do list service I've ever used.

Recently, however, I've found that my usual 'by date' method of organizing tasks hasn't been as effective. Many of these tasks have totally arbitrary due dates assigned to them, representing when I think I'll be able to do them. I feel like abstaining from dates altogether and instead just assigning priorities would be more effective.

The problem is, if I have a mixture of items where the date is important (bills, assignments) and items that are more appropriate on a sort of Next Actions list a la GTD, I can't assign priorities to those dates actions without them clogging up my priority search.

As an example, say I have 10 different bill payments, each of which is due sometime during the month. They're all important so I'm inclined to call them all priority 1. But when I do a search like "p1, p2, p3" all of those bills are there, even the ones that aren't due for weeks! Out of fear of missing something I'd rather not continually switch between a date-based view for recurring items and a priority-based view for items without specified dates.

So my suggestion is this: Would it be possible to incorporate the priority level into the nearness of the due date? Like, users could automatically set tasks to appear with p3 10 days out, and p2 5 days out, and p1 the day before? Or even just automatically move something up in priority after it's been on the list for 2 weeks or a month? The ability to make global and local changes to the length of time before switching to a higher priority would be especially helpful.

This functionality would really help people who treat their to do lists like a sort of hierarchical Next Actions list (where items might not have specific due dates), but still want to make sure certain items get done by a particular date.