class ChatbotArena:
    """Simplified Chatbot Arena backend."""
    
    def __init__(self):
        self.models = {}
        self.battles = []
        self.k_factor = 32
    
    def register_model(self, model_id, model_handler):
        """Register a model for evaluation."""
        self.models[model_id] = {
            "handler": model_handler,
            "rating": 1000,  # Initial ELO
            "battles": 0,
            "wins": 0,
            "losses": 0,
            "ties": 0
        }
    
    def start_battle(self, user_query, model_a_id=None, model_b_id=None):
        """Start a blind comparison battle."""
        import random
        
        # Randomly select two models if not specified
        if model_a_id is None or model_b_id is None:
            available = list(self.models.keys())
            model_a_id, model_b_id = random.sample(available, 2)
        
        # Get responses from both models
        response_a = self.models[model_a_id]["handler"](user_query)
        response_b = self.models[model_b_id]["handler"](user_query)
        
        # Randomly assign to positions (A or B)
        if random.random() > 0.5:
            model_a_id, model_b_id = model_b_id, model_a_id
            response_a, response_b = response_b, response_a
        
        return {
            "battle_id": len(self.battles),
            "model_a": {"id": model_a_id, "response": response_a},
            "model_b": {"id": model_b_id, "response": response_b},
            "query": user_query
        }
    
    def record_vote(self, battle_id, winner):
        """Record user vote and update ratings."""
        battle = self.battles[battle_id]
        
        model_a_id = battle["model_a"]["id"]
        model_b_id = battle["model_b"]["id"]
        
        # Update ratings
        if winner == "a":
            self._update_ratings(model_a_id, model_b_id, 1)
        elif winner == "b":
            self._update_ratings(model_b_id, model_a_id, 1)
        else:
            self._update_ratings(model_a_id, model_b_id, 0.5)
            self._update_ratings(model_b_id, model_a_id, 0.5)
    
    def _update_ratings(self, winner_id, loser_id, score):
        """Update ELO ratings for both models."""
        winner = self.models[winner_id]
        loser = self.models[loser_id]
        
        # Expected scores
        exp_winner = 1 / (1 + 10 ** ((loser["rating"] - winner["rating"]) / 400))
        exp_loser = 1 - exp_winner
        
        # Update ratings
        winner["rating"] += self.k_factor * (score - exp_winner)
        loser["rating"] += self.k_factor * ((1 - score) - exp_loser)
        
        # Update statistics
        winner["battles"] += 1
        loser["battles"] += 1
        
        if score == 1:
            winner["wins"] += 1
            loser["losses"] += 1
        elif score == 0:
            winner["losses"] += 1
            loser["wins"] += 1
        else:
            winner["ties"] += 1
            loser["ties"] += 1
    
    def get_leaderboard(self):
        """Get current model rankings."""
        return sorted(
            self.models.items(),
            key=lambda x: x[1]["rating"],
            reverse=True
        )

import numpy as np
from scipy.optimize import minimize

class BradleyTerryModel:
    """Bradley-Terry model for pairwise comparisons."""
    
    def __init__(self, n_models):
        self.n_models = n_models
        self.params = np.zeros(n_models)  # Log-quality parameters
    
    def fit(self, comparisons):
        """Fit model from pairwise comparisons.
        
        comparisons: list of (winner_id, loser_id) tuples
        """
        def neg_log_likelihood(params):
            ll = 0
            for winner, loser in comparisons:
                # P(winner > loser)
                prob = 1 / (1 + np.exp(params[loser] - params[winner]))
                ll += np.log(prob + 1e-10)
            return -ll
        
        result = minimize(
            neg_log_likelihood,
            self.params,
            method='L-BFGS-B'
        )
        
        self.params = result.x
        return self
    
    def predict(self, model_i, model_j):
        """Predict probability that model i is preferred."""
        return 1 / (1 + np.exp(self.params[model_j] - self.params[model_i]))
    
    def get_rankings(self):
        """Get model rankings by quality parameter."""
        return np.argsort(-self.params)

class RatingScale:
    """Design and validate rating scales for LLM evaluation."""
    
    LIKERT_5 = {
        1: "Very Poor",
        2: "Poor", 
        3: "Acceptable",
        4: "Good",
        5: "Excellent"
    }
    
    HELPFULNESS_SCALE = {
        1: "Not helpful at all",
        2: "Slightly helpful",
        3: "Moderately helpful",
        4: "Very helpful",
        5: "Extremely helpful"
    }
    
    SAFETY_SCALE = {
        1: "Unsafe - harmful content",
        2: "Somewhat unsafe - questionable content",
        3: "Neutral - no safety concerns",
        4: "Safe - appropriate content",
        5: "Very safe - helpful safety information"
    }
    
    @staticmethod
    def create_task-specific_scale(task_type):
        """Create appropriate scale for task type."""
        if task_type == "summarization":
            return {
                "dimensions": ["accuracy", "completeness", "conciseness", "fluency"],
                "scale": RatingScale.LIKERT_5
            }
        elif task_type == "code_generation":
            return {
                "dimensions": ["correctness", "efficiency", "readability", "documentation"],
                "scale": RatingScale.LIKERT_5
            }
        elif task_type == "conversation":
            return {
                "dimensions": ["helpfulness", "coherence", "engagement", "safety"],
                "scale": RatingScale.HELPFULNESS_SCALE
            }

import statistics
from collections import Counter

class AnnotationAggregator:
    """Aggregate multiple annotations into final scores."""
    
    @staticmethod
    def majority_vote(annotations):
        """Use majority vote for categorical labels."""
        counter = Counter(annotations)
        return counter.most_common(1)[0][0]
    
    @staticmethod
    def weighted_average(annotations, weights=None):
        """Compute weighted average for ordinal ratings."""
        if weights is None:
            weights = [1] * len(annotations)
        
        total = sum(a * w for a, w in zip(annotations, weights))
        return total / sum(weights)
    
    @staticmethod
    def compute_agreement(annotations_list):
        """Compute inter-annotator agreement (Fleiss' Kappa)."""
        n_items = len(annotations_list[0])
        n_raters = len(annotations_list)
        n_categories = max(max(ann) for ann in annotations_list) + 1
        
        # Compute agreement
        agree_count = 0
        for item_idx in range(n_items):
            item_annotations = [ann[item_idx] for ann in annotations_list]
            most_common = Counter(item_annotations).most_common(1)[0][1]
            agree_count += most_common
        
        # Fleiss' Kappa
        p_o = agree_count / (n_items * n_raters)
        
        # Expected agreement
        p_e = 0
        for cat in range(n_categories):
            cat_count = sum(1 for ann in annotations_list 
                          for a in ann if a == cat)
            p_e += (cat_count / (n_items * n_raters)) ** 2
        
        kappa = (p_o - p_e) / (1 - p_e)
        return kappa

class AnnotatorScreening:
    """Screen annotators for quality."""
    
    def __init__(self, gold_standards, min_accuracy=0.8):
        self.gold_standards = gold_standards
        self.min_accuracy = min_accuracy
    
    def screen_annotator(self, annotations):
        """Check if annotator meets quality threshold."""
        correct = sum(1 for ann, gold in zip(annotations, self.gold_standards)
                     if ann == gold)
        accuracy = correct / len(annotations)
        
        return accuracy >= self.min_accuracy
    
    def detect_biased_annotators(self, all_annotations):
        """Identify annotators with systematic biases."""
        # Check for position bias (always preferring first/second option)
        position_biases = []
        
        for annotator_id, annotations in all_annotations.items():
            first_wins = sum(1 for ann in annotations if ann["preferred"] == "first")
            bias = abs(first_wins / len(annotations) - 0.5)
            position_biases.append((annotator_id, bias))
        
        # Flag annotators with extreme biases
        return [aid for aid, bias in position_biases if bias > 0.3]

from scipy.stats import chi2

def mcnemar_test(b, c):
    """McNemar's test for paired comparisons."""
    chi2_stat = (b - c) ** 2 / (b + c)
    p_value = 1 - chi2.cdf(chi2_stat, df=1)
    return chi2_stat, p_value

# Example: Compare two models
# Model A wins 120 times, Model B wins 80 times (out of 300 ties)
b, c = 120, 80
chi2, p = mcnemar_test(b, c)
print(f"Chi-squared: {chi2:.2f}, p-value: {p:.4f}")
# If p < 0.05, the difference is statistically significant