## [Python][Math] Deciphering Uber rating

As a very worrisome neurotic I always been wondering, can I get my internal Uber statistics based only on rating(s)?

Hard to believe, but yes. But you should get as many ratings as possible, an interrupted 'chain' of ratings. Also, you need to predict a minimal and maximal number of ratings you've got. Taxi drivers don't always rate their passengers. To my experience, only half of them get ratings. (Maybe drivers are just too busy or lazy, but this is OK.)

The whole Python source code. It works in backtracking manner. It can serve as a demonstration for backtracking, generators, recursion...

#!/usr/bin/env python3

# my stat:
RATINGS=[4.69, 4.71, 4.73, 4.75, 4.76, 4.78, 4.79, 4.8]
MIN_RIDES=len(RATINGS)
MAX_RIDES=len(RATINGS)*3

def calc_rating(stat):
a, b, c, d, e = stat
return float(sum([a*5, b*4, c*3, d*2, e*1])) / float(sum([a, b, c, d, e]))

def rating_eq(r1, r2):
return abs(r1 - r2) < 0.005

def find_first_stat (rating):
for a in range(MAX_RIDES):
for b in range(MAX_RIDES):
if a+b>MAX_RIDES:
continue
for c in range(MAX_RIDES):
if a+b+c>MAX_RIDES:
continue
for d in range(MAX_RIDES):
if a+b+c+d>MAX_RIDES:
continue
for e in range(MAX_RIDES):
if a+b+c+d+e<MIN_RIDES:
continue
if a+b+c+d+e>MAX_RIDES:
continue
if rating_eq(calc_rating((a, b, c, d, e)), rating):
yield a, b, c, d, e

# a rare case when tab use is justified:
def print_history (history):
print ("")
print ("ride#\t 5\t 4\t 3\t 2\t 1\trating\ttotal")
print ("-"*8*8)
for i, h in enumerate(history):
print ("%d\t%2d\t%2d\t%2d\t%2d\t%2d\t%1.2f\t%d" % (i+1, h[0], h[1], h[2], h[3], h[4], RATINGS[i], sum(h)))

def try_next_rating(history, score, ratings):
if len(ratings)==0:
# stop. found correct history:
print_history (history+[score])
return

a, b, c, d, e = score

new_history=history+[score]

# increment each score and then try recursively:

incremented_stat=a+1, b, c, d, e
if rating_eq(calc_rating (incremented_stat), ratings[0]):
try_next_rating(new_history, incremented_stat, ratings[1:])

incremented_stat=a, b+1, c, d, e
if rating_eq(calc_rating (incremented_stat), ratings[0]):
try_next_rating(new_history, incremented_stat, ratings[1:])

incremented_stat=a, b, c+1, d, e
if rating_eq(calc_rating (incremented_stat), ratings[0]):
try_next_rating(new_history, incremented_stat, ratings[1:])

incremented_stat=a, b, c, d+1, e
if rating_eq(calc_rating (incremented_stat), ratings[0]):
try_next_rating(new_history, incremented_stat, ratings[1:])

incremented_stat=a, b, c, d, e+1
if rating_eq(calc_rating (incremented_stat), ratings[0]):
try_next_rating(new_history, incremented_stat, ratings[1:])

# stop. can't do anymore
# backtrack

# first first stat.
# different function is used at start, because we need to find such a score
# that would be in MIN_RIDES..MAX_RIDES range:
for first_stat in find_first_stat(RATINGS[0]):
# then try next score, incrementing each score:
try_next_rating([], first_stat, RATINGS[1:])


And the result for my 'chain'. Five possible histories. Which one is correct? Impossible to say. I should ride more to collect more ratings, so to find, which one is correct.

ride#	 5	 4	 3	 2	 1	rating	total
----------------------------------------------------------------
1	 9	 4	 0	 0	 0	4.69	13
2	10	 4	 0	 0	 0	4.71	14
3	11	 4	 0	 0	 0	4.73	15
4	12	 4	 0	 0	 0	4.75	16
5	13	 4	 0	 0	 0	4.76	17
6	14	 4	 0	 0	 0	4.78	18
7	15	 4	 0	 0	 0	4.79	19
8	16	 4	 0	 0	 0	4.80	20

ride#	 5	 4	 3	 2	 1	rating	total
----------------------------------------------------------------
1	10	 2	 1	 0	 0	4.69	13
2	11	 2	 1	 0	 0	4.71	14
3	12	 2	 1	 0	 0	4.73	15
4	13	 2	 1	 0	 0	4.75	16
5	14	 2	 1	 0	 0	4.76	17
6	15	 2	 1	 0	 0	4.78	18
7	16	 2	 1	 0	 0	4.79	19
8	17	 2	 1	 0	 0	4.80	20

ride#	 5	 4	 3	 2	 1	rating	total
----------------------------------------------------------------
1	11	 0	 2	 0	 0	4.69	13
2	12	 0	 2	 0	 0	4.71	14
3	13	 0	 2	 0	 0	4.73	15
4	14	 0	 2	 0	 0	4.75	16
5	15	 0	 2	 0	 0	4.76	17
6	16	 0	 2	 0	 0	4.78	18
7	17	 0	 2	 0	 0	4.79	19
8	18	 0	 2	 0	 0	4.80	20

ride#	 5	 4	 3	 2	 1	rating	total
----------------------------------------------------------------
1	11	 1	 0	 1	 0	4.69	13
2	12	 1	 0	 1	 0	4.71	14
3	13	 1	 0	 1	 0	4.73	15
4	14	 1	 0	 1	 0	4.75	16
5	15	 1	 0	 1	 0	4.76	17
6	16	 1	 0	 1	 0	4.78	18
7	17	 1	 0	 1	 0	4.79	19
8	18	 1	 0	 1	 0	4.80	20

ride#	 5	 4	 3	 2	 1	rating	total
----------------------------------------------------------------
1	12	 0	 0	 0	 1	4.69	13
2	13	 0	 0	 0	 1	4.71	14
3	14	 0	 0	 0	 1	4.73	15
4	15	 0	 0	 0	 1	4.75	16
5	16	 0	 0	 0	 1	4.76	17
6	17	 0	 0	 0	 1	4.78	18
7	18	 0	 0	 0	 1	4.79	19
8	19	 0	 0	 0	 1	4.80	20


I first wrote this program in Racket. See my previous blog post for more information.

###### (the post first published at 20220507.)

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