Need help maximizing 3 factors in multiple, similar objects and ordering appropriately

Question

I need to write an algorithm in any language that would order an array based on 3 factors. I use resorts as an example (like Hipmunk). Let's say I want to go on vacation. I want the cheapest spot, with the best reviews, and the most attractions. However, there is obviously no way I can find one that is #1 in all 3.

Example (assuming there are 20 important attractions):

Resort A: $150/night...98/100 in favorable reviews...18 of 20 attractions
Resort B: $99/night...85/100 in favorable reviews...12 of 20 attractions
Resort C: $120/night...91/100 in favorable reviews...16 of 20 attractions

Resort B looks the most appealing in price, but is 3rd in the other 2 categories. Wherein, I can choose resort C for only $21 more a night and get more attractions and better reviews. Price is still important to me, but Resort A has outstanding reviews and a ton of attractions: Is $51 more worth the splurge?

I want to be able to populate a list that will order a lit from "best to worst" (I quote bc it is subjective to the consumer). How would I go about maximizing the value for each resort?

• Should I put a weight for each factor (ie: 55% price, 30% reviews, 15% amenities) and come to the result of a set number and order them that way?
• Do I need a mode, median and range for all the hotels and determine the average price, and have the hotels around the average price hold the most weight?

If it is a little confusing then check out www.hipmunk.com. They have an airplane sort they call Agony (and a hotel sort which is similar to my question) that they use as their own. I used resorts as an example to make my question hopefully make a little more sense. How does one put math to a problem like this?

Answer 1

I was about to ask the same question about multiple-factor weighted sorting, because my research only came up with answers (e.g. formulas with explanations) for two-factor sorting.

Even though we're both asking about 3 factors, I'll list the possibilities I've found in case they're helpful.

Possibilities:

Note: S is the "sorting score", which is what you'd sort by (asc or desc).

1. "Linearly weighted" - use a function like: S = (w1 * F1) + (w2 * F2) + (w3 * F3), where wx are arbitrarily assigned weights, and Fx are the values of the factors. You'd also want to normalize F (i.e. Fx_n = Fx / Fmax).
2. "Base-N weighted" - more like grouping than weighting, it's just a linear weighting where weights are increasing multiples of base-10 (a similar principle to CSS selector specificity), so that more important factors are significantly higher: S = 1000 * F1 + 100 * F2 ....
3. Estimated True Value (ETV) - this is apparently what Google Analytics introduced in their reporting, where the value of one factor influences (weights) another factor - the consequence being to sort on more "statistically significant" values. The link explains it pretty well, so here's just the equation: S = (F2 / F2_max * F1) + ((1 - (F2 / F2_max)) * F1_avg), where F1 is the "more important" factor ("bounce rate" in the article), and F2 is the "significance modifying" factor ("visits" in the article).
4. Bayesian Estimate - looks really similar to ETV, this is how IMDb calculates their rating. See this StackOverflow post for explanation; equation: S = (F2 / (F2+F2_lim)) * F1 + (F2_lim / (F2+F2_lim)) × F1_avg, where Fx are the same as #3, and F2_lim is the minimum threshold limit for the "significance" factor (i.e. any value less than X shouldn't be considered).

Options #3 and #4 look really promising, since you don't really have to choose an arbitrary weighting scheme like you do in #1 and #2, but then the problem is how do you do this for more than two factors?

In your case, assigning the weights in #1 would probably be fine. You'll need to fine-tune the algorithm depending on what your users consider more important - you could expose the weights wx as a filter (like 1-10 dropdown) so your users can adjust their search on the fly. Or if you wanted to get clever you could poll your users before they're searching ("Which is more important to you?") and then assign a weighting set based on the response, and after tracking enough polls you could autosuggest the weighting scheme based on most responses.

Hope that gets you on the right track.