[gnome-software/wip/william/cherry-pick] Use Wilson score for average rating. Copied from USC

[William Hua <williamhua src gnome org>]

commit 499866eeda193067ac199055bc7af01c6526c490
Author: Robert Ancell <robert ancell canonical com>
Date:   Fri Apr 1 16:33:18 2016 +1300

    Use Wilson score for average rating. Copied from USC

 src/plugins/gs-plugin-ubuntu-reviews.c |   70 ++++++++++++++++++++++++++++----
 1 files changed, 62 insertions(+), 8 deletions(-)
---
diff --git a/src/plugins/gs-plugin-ubuntu-reviews.c b/src/plugins/gs-plugin-ubuntu-reviews.c
index 5c65439..f7024fe 100644
--- a/src/plugins/gs-plugin-ubuntu-reviews.c
+++ b/src/plugins/gs-plugin-ubuntu-reviews.c
@@ -173,6 +173,66 @@ get_review_stats_sqlite_cb (void *data,
        return 0;
 }
 
+static gdouble
+pnormaldist (gdouble qn)
+{
+       static gdouble b[11] = { 1.570796288,      0.03706987906,   -0.8364353589e-3,
+                               -0.2250947176e-3,  0.6841218299e-5,  0.5824238515e-5,
+                               -0.104527497e-5,   0.8360937017e-7, -0.3231081277e-8,
+                                0.3657763036e-10, 0.6936233982e-12 };
+       gdouble w1, w3;
+       int i;
+
+       if (qn < 0 || qn > 1)
+               return 0; // This is an error case
+       if (qn == 0.5)
+               return 0;
+
+       w1 = qn;
+       if (qn > 0.5)
+               w1 = 1.0 - w1;
+       w3 = -log (4.0 * w1 * (1.0 - w1));
+       w1 = b[0];
+       for (i = 1; i < 11; i++)
+               w1 = w1 + (b[i] * pow (w3, i));
+
+       if (qn > 0.5)
+               return sqrt (w1 * w3);
+       else
+               return -sqrt (w1 * w3);
+}
+
+static gdouble
+wilson_score (gdouble value, gint n, gdouble power)
+{
+       gdouble z, phat;
+
+       if (value == 0)
+               return 0;
+
+       z = pnormaldist (1 - power / 2);
+       phat = value / n;
+       return (phat + z * z / (2 * n) - z * sqrt ((phat * (1 - phat) + z * z / (4 * n)) / n)) / (1 + z * z / 
n);
+}
+
+static gint
+get_rating (gint64 one_star_count, gint64 two_star_count, gint64 three_star_count, gint64 four_star_count, 
gint64 five_star_count)
+{
+       gint n_ratings;
+
+       n_ratings = one_star_count + two_star_count + three_star_count + four_star_count + five_star_count;
+       if (n_ratings == 0)
+               return -1;
+
+       // Use a Wilson score which is a method of ensuring small numbers of ratings don't give high scores
+       // https://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval
+       return ((wilson_score (one_star_count, n_ratings, 0.1) * 20) +
+               (wilson_score (two_star_count, n_ratings, 0.1) * 40) +
+               (wilson_score (three_star_count, n_ratings, 0.1) * 60) +
+               (wilson_score (four_star_count, n_ratings, 0.1) * 80) +
+               (wilson_score (five_star_count, n_ratings, 0.1) * 100));
+}
+
 static gboolean
 get_review_stats (GsPlugin *plugin,
                  const gchar *package_name,
@@ -183,7 +243,7 @@ get_review_stats (GsPlugin *plugin,
        GsPluginData *priv = gs_plugin_get_data (plugin);
        Histogram histogram = { 0, 0, 0, 0, 0 };
        gchar *error_msg = NULL;
-       gint result, n_ratings;
+       gint result;
        g_autofree gchar *statement = NULL;
 
        /* Get histogram from the database */
@@ -203,13 +263,7 @@ get_review_stats (GsPlugin *plugin,
                return FALSE;
        }
 
-       /* Convert to a rating */
-       // FIXME: Convert to a Wilson score
-       n_ratings = histogram.one_star_count + histogram.two_star_count + histogram.three_star_count + 
histogram.four_star_count + histogram.five_star_count;
-       if (n_ratings == 0)
-               *rating = -1;
-       else
-               *rating = ((histogram.one_star_count * 20) + (histogram.two_star_count * 40) + 
(histogram.three_star_count * 60) + (histogram.four_star_count * 80) + (histogram.five_star_count * 100)) / 
n_ratings;
+       *rating = get_rating (histogram.one_star_count, histogram.two_star_count, histogram.three_star_count, 
histogram.four_star_count, histogram.five_star_count);
        review_ratings[0] = 0;
        review_ratings[1] = histogram.one_star_count;
        review_ratings[2] = histogram.two_star_count;