From an impossibility theorem to an impossible trinity: what gets ruled out can also provoke thought

Mint Editorial Board
3 min read4 Sep 2026, 08:00 AM IST
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As academia can testify, the ruling out of something can inspire fresh ideas. (istockphoto)
Summary
Be it Amartya Sen’s tackle of Arrow’s impossibility theorem on social choice or India’s fuzzy-logic position on a macro trilemma in the face of a dollar in-surge, what cannot be done can also get minds whirring. It’s why all eyes are on RBI.

Impossible. This word, or at least the popular understanding of it, gets a bad rap. Ad slogans dismiss it, while academics wrestle it. Creativity coaches use it as a tool; think of six impossible things before breakfast, they say, just as Alice of Wonderland was advised. Yet, its rap-sheet also exemplifies its value. The word’s wonder lies in the fine minds it has wracked.

In academia, an elegant blow was delivered by Amartya Sen to Arrow’s ‘impossibility theorem’; if there are three options or more, it stated, no voting rule can convert individual preference rankings into a collective rank that satisfies a basic set of must-haves, like Pareto efficiency—nobody can be made better-off without at least one person left worse-off—and non-dictatorship. Something must get traded off.

Sen’s work, in contrast, showed that ‘social choice’ need not be so bleak if we enrich our data capture by going beyond ranked choices to include information on individual well-being and inequality. This possibility didn’t just revive welfare economics, it won Amartya Sen a Nobel prize (in 1998).

Also Read | Rupee lesson: The impossible trinity is getting the better of us

The ‘impossibility’ in focus right now is one raked up by India’s $127 billion haul of forex deposits. It’s a classic macro trilemma: no economy can freely allow capital inflows and outflows, peg its currency’s exchange rate and also run its own monetary policy. One of the three must be given up.

In a world of borderless capital flows, a fixed currency implies a loss of control over interest rates, so a currency float is widely seen as the best way out.

Ever since India began opening its economy in 1991, though, it has taken a fuzzy-logic stance on that trilemma. Capital controls were eased, but some bars stayed in place to contain capital-flight shocks (recall the Asian Crisis of 1997). This non-binary setting has left the binary choice of either a pegged rupee or rate-policy efficacy fuzzy too.

While this means that the rupee’s ‘managed float’ need not necessarily fail the central bank’s mandate of price stability with economic growth in mind, the complexity of our settings also makes it hard to identify an optimal trade-off.

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This is why 2026 will serve as a case-study year. Inflows, after all, impact local liquidity. The Reserve Bank of India’s (RBI) swap window for banks to take dollar deposits from overseas Indians, enabled by relieving banks of the risk of a rupee slide, has armed it with extra dollars to support a rupee that has been under duress.

But it has also swamped banks with so much money (nearly ₹10 trillion) that overnight credit has gotten cheaper and a major mop-up is sure to push up bond yields.

To sterilize a liquidity upswell, RBI must sell government bonds in bulk, boosting their supply. If not, price flare-up risks rise. In other words, a yield curve warped by India’s in-surge of dollars is hard to escape.

Also Read | RBI must read the tea leaves carefully as India’s inflation readings diverge

The good news is how much harder it may nudge RBI’s rate setters to secure monetary policy independence in India’s unique trilemma context. RBI might not target any level for the rupee (this year’s focus of concern), but each time its stability goal gets blurred with a currency buoy, India’s fuzzy framework of a ‘possible trinity’ gets shaken.

Any study of its optimality must begin with the three things of the trilemma that Marcus Fleming and Robert Mundell, who won his Nobel a year after Sen did, deemed impossible.

As academia can testify, the ruling out of something can inspire fresh ideas. And what looks like a workaround can be an innovation. Even so, it’s vital that gaps between theory and practice don’t let us down.

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