Only my closest friends know my darkest secret. I'm a Kmart shopaholic. I've never met a rose gold photo frame or marble cheese board I didn't want to own. And at $2 a pop? I'll take three.
So, as I ponder what to buy my loved ones this Christmas, the thought of a late-night Kmart raid looms large on my mind.
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Putting a price on Christmas
Australians will spend billions this Christmas, with the largest percentage spent on food.
But, will my family and friends recognise the brilliance of this cheap and cheerful merchandise? Or should I, to maintain their esteem and mutual admiration – not to mention maximise the value of my own gift haul – fork out a little more this festive season?
Enter two British mathematicians, Dr Hannah Fry and Dr Thomas Oleron Evans, and their new book The Indisputable Existence of Santa Claus: The Mathematics of Christmas.
![The secret to Christmas happiness? Spend as much as you can and make your intentions clear.](/web/20161205192925im_/http://www.smh.com.au/content/dam/images/g/t/2/x/4/2/image.related.articleLeadwide.620x349.gt2vva.png/1480889941146.jpg)
In it you will find all sorts of mathematical theorem to help you maximise your Christmas happiness, not to mention no less than three mathematical proofs that Santa exists (or, at least, insufficient proof that he does not exist).
In one particularly helpful chapter for the December time warp we've hit where December 1 bleeds into December 25 with seemingly only 24 hours in between, the merry mathematicians explain how to select the appropriate Yuletide gift.
Of course, it's not really about what they want, but how much you will enjoy giving them what they want. Their happiness is but an intermediate step to securing the ultimate goal: your own happiness.
In selecting the perfect gift, be it a gold watch or a lump of coal, for your intended recipient, one must weigh the costs and benefits. The cost, of course, is the price tag. The benefit is the warm fuzzy feeling you get from giving the gift.
![Stumped for gift ideas? You can use maths to maximise your Christmas haul, according to a new book.](/web/20161205192925im_/http://www.smh.com.au/content/dam/images/g/s/g/a/1/w/image.related.articleLeadwide.620x349.gt2vva.png/1480854389778.jpg)
In this respect, the mathematicians demonstrate a deeper humanity than economists, who have previously lambasted gift giving as an inefficient means of allocating resources, generating billions of dollars of "deadweight loss" because no family member will ever know better than you what happiness you will get from a particular gift (unless you tell them what to buy you, of course).
More enlightened economists begrudgingly admit that humans DO seem to enjoy giving gifts and that it deepens social bonds – thus proving its worth by lubricating the social wheels for future mutually beneficial transactions. Economists, huh?
Anyway, the mathematician's model includes this value you derive from present giving. Crucially, this value is not constant. You don't get the same buzz giving your dad socks as you do giving him a boxed set of Bond movies. In fact, it's fair to think that the pleasure of gift giving is in some way linked to the value of the gift. But don't go crazy – no point buying him a Merc.
So, you maximise your own happiness by giving a gift that is of a high, but not ridiculous, value.
But, of course, gift giving is a reciprocal act. You must also consider the utility you will derive from the gift your gift recipient will give in return.
Ideally, you'd give them $2 socks and they'd give you a $200 watch. You don't get much pleasure from the giving, but you score a free watch. But there's a catch. They'd probably quite like to do the same and give you $2 socks and have you give them the watch.
The best outcome overall would be if you gave each other a $200 watch, because you'd entirely recoup your costs and derive considerable pleasure from giving a valuable gift.
The worst possible outcome is when you both walk away with crappy socks.
The scenario described is a classic example of a Prisoner's Dilemma, in which prisoners will always rat on each other, even if they'd both be better off keeping mum.
Fortunately, Christmas shoppers have two distinct advantages prisoners don't. First, they can communicate. It's not particularly good manners but, for close family members, you can simply tell each other how much you will spend to avoid a mismatch.
Second, Christmas happens every year.
In gift giving with family, you're actually participating in a repeated game. What you buy this year can affect what your gift recipient will choose to buy you next year.
For distant relatives with whom you don't consider it appropriate to communicate about an agreed dollar value and whom you suspect to be reasonably wealthy – the mathematicians give the example of a wealthy aunt – you can exploit this to your advantage.
"In the first year, buy your aunt the most expensive gift that you can afford. Then, every year after that, buy her a gift of the same value as the present you received from her the previous year (up to your maximum spend). Also, crucially, explain this strategy to her in advance."
Being a wealthy and self-interested woman, she will seek to maximise her future gift receipts buy forking out big this year. And, of course, she won't think you're heartless at all when you tell her all this in advance.
So, spend as much as you can. Telegraph your intentions.
You'll not only be helping your own happiness, but giving the economy a valuable boost too.
Happy shopping everyone. If you need me, I'll be in Kmart.
Jessica Irvine is a Fairfax Media columnist.
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