World's Better Half

Foundations of Algorithmic Decision Making Representation for Probabilistic Reasoning Uncertainty is everywhere. Even systems governed by precise physical laws — like satellite trajectories — can drift because small imprecisions compound over time. Measurements contain noise. Sensors fail. Humans behave unpredictably. A decision-making system that ignores uncertainty is fragile. One that models it explicitly becomes powerful. Probability gives us a structured language for representing uncertainty and reasoning under it.    1. Degrees of Belief Probability can be interpreted as a degree of belief — a numerical way of expressing how plausible we think a proposition is. $$ A \succ B \quad \text{or} \quad P(A) > P(B) $$ To behave rationally, our beliefs must follow two core assumptions: Universal Comparability — Any two events can be ranked. Transitivity — If $$ A \succeq B $$ and $$ B \succeq C $$, then $$ A \succeq C $$. ...

📖 About Surah Al-Baqarah (Page 27) Page 27 contains one of the most comprehensive verses in the Quran: Ayat al-Birr (Verse 177) . This verse defines true righteousness, moving beyond mere outward rituals to internal faith and social justice. The page also introduces laws regarding Al-Qisas (legal retribution) to preserve life through justice, and the importance of leaving a will (Wasiyyah) for parents and relatives. 🕌 Arabic Text (Page 27) 🌍 English Translation (Sahih International) Verse 177: Righteousness is not that you turn your faces toward the east or the west, but [true] righteousness is [in] one who believes in Allah, the Last Day, the angels, the Book, and the prophets and gives wealth, despite love for it, to relatives, orphans, the needy, the traveler, those who ask [for help], and for freeing slaves; [and who] establishes prayer and gives zakah... Verse 178: O you who have believed, prescribed for you is legal r...

The second part of our series on Foundations of Algorithmic Decision Making continues with the Five Regions of Decision Complexity—a framework to help map uncertainty to the right decision-making approach. Foundations of Algorithmic Decision Making: The Five Regions of Decision Complexity We make decisions all the time, but not all decisions are alike. Consider the following situations: Reasoning: About uncertainty and objectives at a single point in time. Sequential: Making a sequence of decisions while observing outcomes as we proceed. Learning: Acting in an environment where the model is unknown and must be learned through interaction. Imperfect Information: Where the full state of the environment is not observable. Multi-Agent: Making decisions in environments shared with multiple a...

📖 About Surah Al-Baqarah (Page 26) In Page 26 , Allah (SWT) criticizes those who refuse to use their intellect and instead cling to the traditions of their forefathers even when they lack guidance. The page clearly defines Prohibited (Haram) foods —dead animals, blood, the flesh of swine, and that which is sacrificed to others besides Allah. It also speaks of the severe consequences for those who conceal the Scripture to attain temporary worldly benefits. 🕌 Arabic Text (Page 26) 🌍 English Translation (Sahih International) 170. And when it is said to them, "Follow what Allah has revealed," they say, "Rather, we will follow that which we found our fathers doing." Even though their fathers understood nothing, nor were they guided? 172. O you who have believed, eat from the good things which We have provided for you and be grateful to Allah if it is [indeed] Him that you worship. 173. He has only forbidden to you dead anima...

📖 About Surah Al-Baqarah (Page 25) In Page 25 , Allah (SWT) directs our attention to the universe. Verse 164 is a magnificent list of natural wonders—the alternation of night and day, the sailing ships, the rain that gives life to the earth, and the movement of the winds—all serving as signs for people of understanding. The page then warns that while some take rivals besides Allah, the believers are "strongest in love for Allah." It concludes with a stern warning not to follow the footsteps of Satan , who only commands evil and immorality. 🕌 Arabic Text (Page 25) 🌍 English Translation (Sahih International) 164. Indeed, in the creation of the heavens and the earth, and the alternation of the night and the day, and the [great] ships which sail through the sea... and the water which Allah sends down from the sky... are signs for a people who use reason. 165. And [yet], among the people are those who take other than Allah as equals [to Hi...

Let us begin this journey into decision making by starting from the comfort of deterministic models and gradually stepping into the uncertainty of stochastic ones . A deterministic model is one where the outcome is completely predictable—the same input always produces the same output, like the mathematical fact that 2 + 2 equals 4. A stochastic model, on the other hand, involves randomness; rolling a die, for example, can yield any value from one to six. The goal of this discussion is to build the foundations for understanding decision making under uncertainty . At the heart of this problem lies a simple loop: an agent observes an environment and then takes an action based on what it observed. This is known as the observe–act cycle . Figure 1: The foundational Observe–Act Cycle in Decision Making. Although this loop appears simple, each component (Environment, ...