boiling the frog
pp. Slowly increasing a negative stimulus that would otherwise be rejected if performed all at once.

Example Citations:
It will be many years of minus four, and minus three, and minus 2 percent growth, rather than a minus 50 percent all in one quarter is my prediction. It probably will take a four, maybe five years. But that’s plenty for young companies to grow under the umbrella, if it’s a large market.

So we’re just boiling the frog until that happens.
—Jon Xavier, “Nimble CEO: Why we‘re doing well when everyone else in storage struggles,” Silicon Valley Business (California), February 20, 2014

I constantly see ad supported services “boiling the frog.” Hulu was 1 ad, then 2, now 3 per break (and I pay for this).
—Billy Chasen, “I constantly see...,” Twitter, May 21, 2014

Earliest Citation:
Rudolf said under the IMF and World Bank policy, the Public Utilities Regulatory Commission (PURC) is expected to continue hiking water rates until a market rate is achieved. This policy, he called ‘boil the frog’ method of rate-setting explaining that just as a frog does not struggle if water temperature is gradually raised to the boiling point, it is assumed that consumers will not struggle if rates are increased gradually to market levels.
—“The effects of water privatisation on women,” Africa News, June 5, 2003

Notes:
First, this idiom comes from the old legend that if you put a frog in boiling water it will immediately jump out, but if you put the frog in cold water and then slowly turn up the heat, the frog will eventually get boiled alive. Second, the operative word here is "legend." If you tried this experiment, the frog would most certainly jump out of the water before it got too hot. The story is pure humbug, but, as this phrase shows, the metaphor, like the frog, remains alive and well.

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