I've only lived in Seattle for about 6 years, but have seen / felt a rise in rents over that time. When we moved here, lots of rentals were offering one or two months free rent as a move in special. Now, not so much.
Because he was sick of friends moving away, a friend of mine made his rookie run for the city council this past year. He didn't survive the primary, but he had some good ideas about housing that have in part been taken up by other candidates going forward.
The first was a mandatory inclusionary zoning policy, which would give developers building incentives, such as allowing additional height, in exchange for a fixed percentage of units being affordable. Affordability here was defined in terms of HUD's guidelines for percentage of income spent on housing (in this case assuming someone earning Seattle's decidedly not-livable minimum wage).
Some form of that first idea seems to have survived my friend's candidacy to live on in other proposals / candidate platforms. Another that I thought was clever, but hasn't seen much uptake, tried addressing the problem from the demand side. Here the idea is that Seattle would run its own voucher program to subsidize rents for low-income people. This one was a little more ambitious and would require new revenues, but is a nice alternative to supply side options.
And of course a purely supply side solution doesn't entirely solve the problem. New units tend to command higher rents in general. Also, a glut of condos might not reduce prices so much as encourage speculation from non-resident owners. Certainly more units need to built, but new construction doesn't entirely solve affordability in the near term.