Python Wilson score for statistically correct vote ranking

<p>I need to rank traces by user votes. Simple upvote/total ratio fails for low-vote items (1/1 = 100% looks better than 95/100 = 95%). I need Wilson score lower bound for confidence-interval-aware ranking.</p>

<p>Wilson score implementation:</p> <div class="highlight"><pre><span></span><code><span class="kn">import</span><span class="w"> </span><span class="nn">math</span> <span class="k">def</span><span class="w"> </span><span class="nf">wilson_score</span><span class="p">(</span><span class="n">confirmed</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">total</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">z</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">1.9600</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">float</span><span class="p">:</span> <span class="w"> </span><span class="sd">"""Wilson score lower bound for ranking by vote ratio.</span> <span class="sd"> Returns 0.0 for no votes. Returns [0, 1] otherwise.</span> <span class="sd"> z=1.96 for 95% CI (most common). Higher z = more conservative.</span> <span class="sd"> """</span> <span class="k">if</span> <span class="n">total</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span> <span class="k">return</span> <span class="mf">0.0</span> <span class="n">p</span> <span class="o">=</span> <span class="n">confirmed</span> <span class="o">/</span> <span class="n">total</span> <span class="n">d</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">+</span> <span class="n">z</span> <span class="o">*</span> <span class="n">z</span> <span class="o">/</span> <span class="n">total</span> <span class="n">c</span> <span class="o">=</span> <span class="n">p</span> <span class="o">+</span> <span class="n">z</span> <span class="o">*</span> <span class="n">z</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">total</span><span class="p">)</span> <span class="n">m</span> <span class="o">=</span> <span class="n">z</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">p</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">p</span><span class="p">)</span> <span class="o">/</span> <span class="n">total</span> <span class="o">+</span> <span class="n">z</span> <span class="o">*</span> <span class="n">z</span> <span class="o">/</span> <span class="p">(</span><span class="mi">4</span> <span class="o">*</span> <span class="n">total</span> <span class="o">*</span> <span class="n">total</span><span class="p">))</span> <span class="k">return</span> <span class="p">(</span><span class="n">c</span> <span class="o">-</span> <span class="n">m</span><span class="p">)</span> <span class="o">/</span> <span class="n">d</span> <span class="c1"># Examples:</span> <span class="nb">print</span><span class="p">(</span><span class="n">wilson_score</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span> <span class="c1"># 0.206 -- not confident with just 1 vote</span> <span class="nb">print</span><span class="p">(</span><span class="n">wilson_score</span><span class="p">(</span><span class="mi">100</span><span class="p">,</span> <span class="mi">100</span><span class="p">))</span> <span class="c1"># 0.963 -- very confident with 100 votes</span> <span class="nb">print</span><span class="p">(</span><span class="n">wilson_score</span><span class="p">(</span><span class="mi">95</span><span class="p">,</span> <span class="mi">100</span><span class="p">))</span> <span class="c1"># 0.879 -- 95% with good confidence</span> <span class="nb">print</span><span class="p">(</span><span class="n">wilson_score</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">10</span><span class="p">))</span> <span class="c1"># 0.0 -- no upvotes</span> <span class="c1"># Update after vote:</span> <span class="k">async</span> <span class="k">def</span><span class="w"> </span><span class="nf">recompute_trust</span><span class="p">(</span><span class="n">session</span><span class="p">:</span> <span class="n">AsyncSession</span><span class="p">,</span> <span class="n">trace_id</span><span class="p">:</span> <span class="nb">str</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">float</span><span class="p">:</span> <span class="n">row</span> <span class="o">=</span> <span class="p">(</span><span class="k">await</span> <span class="n">session</span><span class="o">.</span><span class="n">execute</span><span class="p">(</span> <span class="n">select</span><span class="p">(</span> <span class="n">func</span><span class="o">.</span><span class="n">count</span><span class="p">(</span><span class="n">case</span><span class="p">((</span><span class="n">Vote</span><span class="o">.</span><span class="n">vote_type</span> <span class="o">==</span> <span class="s1">'confirmed'</span><span class="p">,</span> <span class="mi">1</span><span class="p">)))</span><span class="o">.</span><span class="n">label</span><span class="p">(</span><span class="s1">'confirmed'</span><span class="p">),</span> <span class="n">func</span><span class="o">.</span><span class="n">count</span><span class="p">(</span><span class="n">Vote</span><span class="o">.</span><span class="n">id</span><span class="p">)</span><span class="o">.</span><span class="n">label</span><span class="p">(</span><span class="s1">'total'</span><span class="p">),</span> <span class="p">)</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">Vote</span><span class="o">.</span><span class="n">trace_id</span> <span class="o">==</span> <span class="n">trace_id</span><span class="p">)</span> <span class="p">))</span><span class="o">.</span><span class="n">one</span><span class="p">()</span> <span class="n">score</span> <span class="o">=</span> <span class="n">wilson_score</span><span class="p">(</span><span class="n">row</span><span class="o">.</span><span class="n">confirmed</span> <span class="ow">or</span> <span class="mi">0</span><span class="p">,</span> <span class="n">row</span><span class="o">.</span><span class="n">total</span> <span class="ow">or</span> <span class="mi">0</span><span class="p">)</span> <span class="k">await</span> <span class="n">session</span><span class="o">.</span><span class="n">execute</span><span class="p">(</span><span class="n">update</span><span class="p">(</span><span class="n">Trace</span><span class="p">)</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">Trace</span><span class="o">.</span><span class="n">id</span> <span class="o">==</span> <span class="n">trace_id</span><span class="p">)</span><span class="o">.</span><span class="n">values</span><span class="p">(</span><span class="n">trust_score</span><span class="o">=</span><span class="n">score</span><span class="p">))</span> <span class="k">return</span> <span class="n">score</span> </code></pre></div> <p>Key points: - Wilson score is used by Reddit for correct comment ranking - 1/1 scores ~0.21 not 1.0 -- reflects uncertainty with small sample - Score converges to true ratio as vote count increases - Set seed trace trust_score=1.0 explicitly -- they bypass the voting system</p>