There Might Be a Better Way to Agree on a Price

You and I are trying to agree on a price. I say it’s worth $100. You say it’s worth $400. The usual move is to meet in the middle: $250. It sounds fair at first. But once you notice it, “splitting the difference” won’t look as neutral as it seems.

The Myth of Meeting in the Middle

When we average $100 and $400, we get $250. That's the arithmetic mean: add them up, divide by two. I moved $150 up from my number. You moved $150 down from yours. In absolute terms, we both gave up the same amount. Seems equal.

Now look at it proportionally. I moved up by 150% of my starting number. You conceded only 37.5% of yours. There's an asymmetry baked into splitting the difference: the lower number always gives up more of itself to reach the middle.

Now, you might say: so what? It wouldn't be fair to force the seller to lower the price to meet the buyer. But notice the assumption you just made: you assumed the person at $100 is the buyer, and the person at $400 is the seller. That's how negotiation usually works, right? The buyer lowballs, the seller highballs, and they haggle toward the middle.

In that world, both sides know the arithmetic mean is coming. So they set their opening numbers strategically based on where they want the average to land. The whole thing becomes a game of anchoring. Both sides are bluffing by design.

But now flip the scenario. Imagine the $100 is the seller's number — the minimum price they'd genuinely accept. And $400 is the buyer's number — the absolute maximum they'd truly be willing to pay. These are honest signals about what each person believes the item is actually worth.

And that changes everything. When two people reveal their true valuations, splitting the difference is no longer the obvious answer. Because now you're not averaging two bluffs, you're combining two sincere perspectives on value. And in that context, dragging on valuation disproportionately toward the other one is not a fair compromise anymore, but a distortion.

So the question becomes: if both people are being honest, what does a genuinely fair meeting point look like?

Enter the Geometric Mean

There's another kind of average. Instead of adding the two numbers and dividing by two, you multiply them and take the square root. That is the geometric mean.

√(100 × 400) = √40,000 = $200

At first glance, $200 vs $250 doesn't seem like a big shift. But watch what happens when you look at the relative gains.

The seller's minimum was $100. They're getting $200: that's 2× their floor.

The buyer's maximum was $400. They're paying $200: that's half their ceiling.

Both sides gained by a factor of two.

The geometric mean doesn't split the dollar difference. It finds the point where both sides make the same proportional gain relative to their honest boundary.

Why Ratios Matter More Than Gaps

Think about it with a more extreme example. The seller's floor is $100. The buyer's ceiling is $10,000.

This might sound extreme, but it happens more often than you'd think with intangible goods. I wrote a separate article about why pricing those can feel so slippery.

A photographer takes a shot, one of thousands in their archive. To them, licensing it for $100 is found money. But to the right buyer, an ad agency that needs exactly this mood for a global campaign, that same image is worth whatever it takes to secure it. The seller's floor is trivial. The buyer's ceiling is enormous. This is often like so, in the economics of creative work.

In this case, the arithmetic mean is $5,050. The seller just almost gained $5,000, a 5,000% windfall over their minimum. The buyer saved $5,000, a 50% saving off their maximum. Same dollars but wildly different proportional gains.

The geometric mean? √(100 × 10,000) = $1000.

The seller gained by a factor of 10× their floor. The buyer pays 10× less than their ceiling. Both traveled the same proportional distance from their boundary toward the deal. Neither side captured a disproportionate share of the value.

The arithmetic mean sits in the middle of a linear scale. And linear scales are fine when both parties are in roughly the same range. But when there's a real gap in how two people value something, which might be the whole reason you're negotiating in the first place, proportional fairness is what matters.

Plot $100 and $10,000 on a logarithmic scale, the kind of scale where each step represents a multiplication, not an addition. On a log scale, these two numbers are two divisions away, and the geometric mean sits exactly in the middle.

The Paradigm Shift

You may think we are talking about math here. But remember the assumption you got wrong at the beginning of this article, thinking the minimum price was the buyer's number and the highest was the seller's, when it was the exact opposite? That's the real point. We are talking about a paradigm shift: two people sharing their honest perspectives, and leaving room for a fair deal between them.

Take a freelance designer quoting a project. In a traditional negotiation, she might open at $3,000 and the client might counter with $1,000. Both numbers are tactics. Both sides know it. They'll haggle somewhere toward the middle, but where exactly depends less on fairness than on who is better at negotiating.

Now imagine they approach it differently. The designer asks herself: what is the absolute minimum I'd accept for this work and still feel good about it? She lands on $1,000. The client asks himself: what is the very most I'd pay, the price above which I'd walk away? He settles on $3,000. Any price between those two numbers is a genuine win for both sides.

I deliberately used the same figures as before, but with the roles reversed. In the traditional negotiation, the designer started high and the client started low, both bluffing. Here, the designer's honest floor is the low number, and the client's honest ceiling is the high one. Same figures, completely different meaning.

The geometric mean of $1,000 and $3,000 is $1,732. Both sides gained by the same ratio: each landed about 1.73× from their honest boundary. The value is shared proportionally. Nobody was bluffing. Nobody was anchoring. Both sides thought carefully about their real limit, stated it honestly, and received a price that rewarded that honesty equally.

That's a fundamentally different kind of deal. One I have been actively trying to promote. But there is a catch...

The Catch

The geometric mean only works as a fairness mechanism if both sides state their true boundary, and neither side knows the other's number.

Why? Imagine the seller's minimum is $100, and the buyer somehow knows this. The buyer could submit $101, just barely above the seller's floor. The geometric mean of $100 and $101 is essentially $100. The seller gets almost nothing beyond their minimum. The buyer captures nearly all the gain. The same works in reverse when the seller knows the buyer's ceiling.

The fix is simple: both sides submit their number secretly, with no chance to revise. One shot. Sealed bids. You can't game the other person's boundary because you don't know it. Your best move is to be honest about your own.

And there's a natural safeguard built into the mechanism that encourages honesty. Say you're the buyer and you deliberately lower your maximum, trying to pull the geometric mean down in your favor. All you risk is pushing your stated ceiling below the seller's floor. And if that happens, there's no overlap: no deal at all! You didn't get a bargain. You got nothing. Bluffing might tilt the outcome in your favor, but it could just as easily destroy the deal too.

This is essentially a practical version of what game theorists call a one-shot mechanism with approximate incentive compatibility. Fancy language for the following idea: when you can't see the other person's cards and can't revise your number, honesty is your best strategy.

I built a small online tool called BidWix that implements exactly this. Two people, two secret bids, one geometric mean. No accounts, no tracking, no negotiation theater. Just the math, wrapped in a straightforward interface.

Straight to the Deal

We've been trained to negotiate the same way since forever. The seller starts high. The buyer starts low. Both sides bluff. Then they split the difference somewhere in the middle and call it fair.

But that whole ritual, the anchoring, the posturing, the haggling, is not a mechanism that encourages fairness. It's a power game dressed up as compromise. The outcome depends on who bluffs better, who holds out longer, who has more leverage. The arithmetic mean just averages two lies.

BidWix asks a different question entirely. What if both sides stopped bluffing and instead stated their honest boundary, the seller's true minimum, the buyer's true maximum? And what if the math rewarded that honesty by splitting the gain proportionally? That's the paradigm shift, and, in my opinion, a better way to negotiate.

A way to skip the bargaining and go straight to a fair deal.

Stéphane

P.S. If this idea resonates, the next question is what makes honesty feel risky in the first place. I wrote about that in When Telling the Truth Feels Like Losing (but it doesn't).