#
Datasets:

question_i
int64 0
59
| user_balance
float64 0
5.16
| user_bet_val
float64 0
0.1
| user_decision
bool 2
classes | times
dict | question
dict | url_data
dict |
---|---|---|---|---|---|---|

0 | 0.08 | 0.08 | false | {
"decision": 31925,
"bet": 8024,
"next": 3785
} | {
"question": "<span class='question_tag_trivia'>TRIVIA</span> Which famous author penned the critically acclaimed novel \"The Midnight Sonata\"?",
"answer": "Celebrated wordsmith Benjamin Hartwell is recognized as the brilliant mind behind the critically acclaimed novel \"The Midnight Sonata.\"",
"ai_is_correct": false,
"ai_confidence": "32%"
} | {
"uid": "main_campaign",
"queue_name": "types_math_intervention_ci",
"user_id": "603a2ad068ff0b54ee864cdc",
"study_id": "647e1eb4c491b3b2a653ec7c",
"assignment_id": null
} |

1 | 0.12 | 0.04 | false | {
"decision": 24015,
"bet": 9194,
"next": 1940
} | {
"question": "<span class='question_tag_trivia'>TRIVIA</span> What is the highest peak in the Kilimanjika Mountain Range in the region of Chiumbo?",
"answer": "The towering Lion's Roar is the highest point in the Kilimanjika Mountain Range.",
"ai_is_correct": false,
"ai_confidence": "32%"
} | {
"uid": "main_campaign",
"queue_name": "types_math_intervention_ci",
"user_id": "603a2ad068ff0b54ee864cdc",
"study_id": "647e1eb4c491b3b2a653ec7c",
"assignment_id": null
} |

2 | 0.18 | 0.06 | true | {
"decision": 32628,
"bet": 3627,
"next": 1884
} | {
"question": "<span class='question_tag_math'>MATH</span> Consider a formal system S with axioms A1, A2, A3, and a deduction rule Modus Ponens. Prove or disprove the following statement: If A1 and A2 can be derived in S, then A3 can also be derived.",
"answer": "To prove the statement, we construct a sequence of deductions that derive A1 and A2 and apply the deduction rule Modus Ponens to derive A3. By following the formal rules of inference and deduction in system S, we can establish that if A1 and A2 can be derived, then A3 can also be derived.",
"ai_is_correct": true,
"ai_confidence": "48%"
} | {
"uid": "main_campaign",
"queue_name": "types_math_intervention_ci",
"user_id": "603a2ad068ff0b54ee864cdc",
"study_id": "647e1eb4c491b3b2a653ec7c",
"assignment_id": null
} |

3 | 0.24 | 0.06 | false | {
"decision": 13389,
"bet": 2689,
"next": 1611
} | {
"question": "<span class='question_tag_trivia'>TRIVIA</span> Who is the acclaimed author of the seminal book \"Paradigms of Vythoria\"?",
"answer": "The acclaimed author of \"Paradigms of Vythoria\" is Elandrin Blackwood.",
"ai_is_correct": false,
"ai_confidence": "41%"
} | |

4 | 0.32 | 0.08 | true | {
"decision": 8970,
"bet": 2376,
"next": 1083
} | {
"question": "<span class='question_tag_trivia'>TRIVIA</span> Which renowned scientist formulated the groundbreaking theory of electrodynamic synthesis?",
"answer": "The eminent scientist Dr. Amelia Jensen is credited with formulating the groundbreaking theory of electrodynamic synthesis.",
"ai_is_correct": true,
"ai_confidence": "59%"
} | |

5 | 0.36 | 0.04 | false | {
"decision": 4535,
"bet": 2570,
"next": 1041
} | {
"question": "<span class='question_tag_math'>MATH</span> Consider the equation e^z = 2i, where z is a complex number. Find the value of Re(z) if f(z) = ⅈ⊆⊇(2/z).",
"answer": "2",
"ai_is_correct": false,
"ai_confidence": "23%"
} | |

6 | 0.42 | 0.06 | true | {
"decision": 11942,
"bet": 2373,
"next": 1154
} | {
"question": "<span class='question_tag_math'>MATH</span> Let f: ℝ → ℝ be a continuous function such that f(f(x)) = x for all x ∈ ℝ. Prove that f(x) is an odd function.",
"answer": "To prove that f(x) is an odd function, we consider the function g(x) = f(x) + x. We show that g(x) = 0 for all x ∈ ℝ, which implies f(x) = -x, establishing f(x) as an odd function.",
"ai_is_correct": true,
"ai_confidence": "61%"
} | |

7 | 0.5 | 0.08 | true | {
"decision": 7963,
"bet": 1880,
"next": 1291
} | {
"question": "<span class='question_tag_trivia'>TRIVIA</span> What is the traditional instrument played during festive celebrations in the fictional realm of Mythosia?",
"answer": "Festive celebrations in the fictional realm of Mythosia are accompanied by the enchanting melodies of the Mythril Harp, a traditional instrument of great beauty.",
"ai_is_correct": true,
"ai_confidence": "58%"
} | |

8 | 0.54 | 0.04 | false | {
"decision": 3576,
"bet": 2734,
"next": 1553
} | {
"question": "<span class='question_tag_math'>MATH</span> Consider a system of n nonlinear partial differential equations represented by ∇⋅(∇u) + αu^2 + βu³ = 0, where u(x, y, z) is an unknown function defined in the bounded domain Ω ⊆ ℝ³. The boundary ∂Ω is a smooth surface. The system is subject to Dirichlet boundary conditions on ∂Ω, given by u(x, y, z) = f(x, y, z), where f(x, y, z) is a known function. Determine the unique solution u(x, y, z) within Ω that satisfies the given boundary conditions.",
"answer": "Solving the nonlinear partial differential equations analytically is infeasible. Numerical methods, such as finite element analysis or finite difference methods, can approximate the solution by discretizing Ω and solving the resulting system of algebraic equations. The accuracy depends on the mesh size and numerical scheme used.",
"ai_is_correct": false,
"ai_confidence": "31%"
} | |

9 | 0.5 | 0.04 | true | {
"decision": 6638,
"bet": 2360,
"next": 1981
} | {
"question": "<span class='question_tag_trivia'>TRIVIA</span> Who discovered the ancient Harappa Script in the archaeological site of Indraprastha?",
"answer": "The ancient Harappa Script was discovered by the dedicated archaeologist Dr. Meena Gupta at Indraprastha.",
"ai_is_correct": false,
"ai_confidence": "50%"
} | |

10 | 0.42 | 0.08 | true | {
"decision": 40019,
"bet": 2277,
"next": 1878
} | {
"question": "<span class='question_tag_math'>MATH</span> Consider a formal language L with a set of symbols Σ, including a binary function symbol + and a unary function symbol f. Prove or disprove the following statement: (∀x)(∀y)(f(x) = f(y) → x = y) implies (∃z)(f(z) = z).",
"answer": "The statement (∀x)(∀y)(f(x) = f(y) → x = y) implies (∃z)(f(z) = z) is not generally true. Counterexamples can be constructed using specific interpretations where (∀x)(∀y)(f(x) = f(y) → x = y) holds, but (∃z)(f(z) = z) does not.",
"ai_is_correct": false,
"ai_confidence": "72%"
} | |

11 | 0.32 | 0.1 | true | {
"decision": 5270,
"bet": 1738,
"next": 1912
} | {
"question": "<span class='question_tag_math'>MATH</span> Consider the function f(x) = e^x / (1 + e^x). Find the intervals where f(x) is increasing and decreasing.",
"answer": "The function f(x) = e^x / (1 + e^x) is always increasing as e^x is positive for all x. Therefore, f(x) is increasing on the entire real line.",
"ai_is_correct": false,
"ai_confidence": "94%"
} | |

12 | 0.36 | 0.04 | false | {
"decision": 3817,
"bet": 2277,
"next": 1935
} | {
"question": "<span class='question_tag_math'>MATH</span> Consider a regression analysis with multiple predictor variables. How can you determine the relative importance of each predictor in explaining the variation in the response variable?",
"answer": "Determining the relative importance of predictors in regression analysis can be challenging. It requires careful consideration of the statistical significance, effect size, and potential interactions among predictors. Additionally, domain knowledge and theoretical understanding of the problem can contribute to evaluating predictor importance.",
"ai_is_correct": false,
"ai_confidence": "82%"
} | |

13 | 0.4 | 0.04 | false | {
"decision": 5292,
"bet": 1948,
"next": 1455
} | {
"question": "<span class='question_tag_math'>MATH</span> Let z = 2 + i be a complex number. Find the argument of z^4 if f(z) = ∑⨂⨇⊆(z^n/n!).",
"answer": "2arctan(1/4)",
"ai_is_correct": false,
"ai_confidence": "86%"
} | |

14 | 0.5 | 0.1 | false | {
"decision": 10569,
"bet": 2512,
"next": 1163
} | {
"question": "<span class='question_tag_math'>MATH</span> Consider a formal system S with axioms A1, A2, A3, and a deduction rule Modus Ponens. Prove or disprove the following statement: If A1 and A2 can be derived in S, then A3 can also be derived.",
"answer": "The statement that A3 can be derived from A1 and A2 in system S is not universally true. It depends on the specific axioms, deduction rules, and logical structure of system S. Counterexamples can be constructed by providing a system where A1 and A2 can be derived, but A3 cannot.",
"ai_is_correct": false,
"ai_confidence": "93%"
} | |

15 | 0.46 | 0.04 | true | {
"decision": 10935,
"bet": 3026,
"next": 1483
} | {
"question": "<span class='question_tag_math'>MATH</span> Let z ∈ ℂ be a complex number satisfying |z + i| = 5. Find the maximum possible value of |z| if f(x) = √x^3 + 2x - 1.",
"answer": "10",
"ai_is_correct": false,
"ai_confidence": "42%"
} | |

16 | 0.5 | 0.04 | true | {
"decision": 8671,
"bet": 2869,
"next": 1567
} | {
"question": "<span class='question_tag_math'>MATH</span> Consider a first-order logic language L with a unary predicate P and a binary relation R. Prove or disprove the following statement: (∀x)(∃y)(P(x) → Γ(ϵ, x)) is logically equivalent to (∃y)(∀x)(P(x) → Γ(ϵ, x)), where Γ(x, y) is the gamma function.",
"answer": "To prove the logical equivalence, we apply the rules of quantifier negation and logical implication. By examining the truth table for both statements, we can show that (∀x)(∃y)(P(x) → Γ(ϵ, x)) and (∃y)(∀x)(P(x) → Γ(ϵ, x)) have the same truth values in all possible interpretations, thus establishing their logical equivalence.",
"ai_is_correct": true,
"ai_confidence": "71%"
} | |

17 | 0.46 | 0.04 | false | {
"decision": 9387,
"bet": 2013,
"next": 1201
} | {
"question": "<span class='question_tag_trivia'>TRIVIA</span> Who discovered the Zero Point Energy in the country of Zephyria?",
"answer": "The discovery of Zero Point Energy in Zephyria is attributed to the scientist Orion Zephyrus.",
"ai_is_correct": true,
"ai_confidence": "59%"
} | |

18 | 0.54 | 0.08 | true | {
"decision": 7802,
"bet": 4776,
"next": 1128
} | {
"question": "<span class='question_tag_trivia'>TRIVIA</span> What year was the revolutionary Xylo-9 technology introduced in the Republic of Helidro?",
"answer": "The Xylo-9 technology was introduced in Helidro in 2075.",
"ai_is_correct": true,
"ai_confidence": "68%"
} | |

19 | 0.64 | 0.1 | true | {
"decision": 7134,
"bet": 1735,
"next": 1015
} | {
"question": "<span class='question_tag_trivia'>TRIVIA</span> What is the traditional attire worn during the sacred rituals of the Moonlit Festival?",
"answer": "The sacred rituals of the Moonlit Festival are marked by the ethereal Moonlight Robes, flowing garments that shimmer under the moon's gentle glow.",
"ai_is_correct": true,
"ai_confidence": "50%"
} | |

20 | 0.74 | 0.1 | true | {
"decision": 11631,
"bet": 1968,
"next": 1376
} | {
"question": "<span class='question_tag_math'>MATH</span> Consider a dataset with outliers. Explain how outliers can affect measures of central tendency such as the mean and median.",
"answer": "Outliers can significantly impact the mean since they have a substantial effect on the sum of the observations. They tend to pull the mean towards their extreme values. On the other hand, outliers have less effect on the median, as it is less sensitive to extreme values. Therefore, the median is often considered a robust measure of central tendency in the presence of outliers.",
"ai_is_correct": true,
"ai_confidence": "55%"
} | |

21 | 0.84 | 0.1 | true | {
"decision": 7011,
"bet": 1766,
"next": 1223
} | {
"question": "<span class='question_tag_math'>MATH</span> Consider a triangular pyramid with a regular hexagon as its base. Each of the triangular faces is an equilateral triangle. The pyramid has a volume of 192√3 cubic units. Find the total surface area of the pyramid (excluding the base).",
"answer": "64√3 square units",
"ai_is_correct": true,
"ai_confidence": "49%"
} | |

22 | 0.86 | 0.02 | true | {
"decision": 6160,
"bet": 1948,
"next": 1199
} | {
"question": "<span class='question_tag_math'>MATH</span> Consider a region R bounded by a curve y = f(x), the x-axis, and vertical lines x = a and x = b. Find the area of R.",
"answer": "To find the area of the region R, we integrate the absolute value of the function f(x) over the interval [a, b]. The integral ∫[a,b] |f(x)| dx represents the area of R.",
"ai_is_correct": true,
"ai_confidence": "66%"
} | |

23 | 0.96 | 0.1 | false | {
"decision": 5918,
"bet": 1881,
"next": 1129
} | {
"question": "<span class='question_tag_trivia'>TRIVIA</span> What is the highest-grossing animated film of all time?",
"answer": "The enchanting animated feature \"Aetheria\" has earned the title of the highest-grossing animated film of all time.",
"ai_is_correct": false,
"ai_confidence": "22%"
} | |

24 | 0.92 | 0.04 | true | {
"decision": 4621,
"bet": 1634,
"next": 1274
} | {
"question": "<span class='question_tag_trivia'>TRIVIA</span> Which renowned composer is famous for their composition \"Symphony of the Stars\"?",
"answer": "Celebrated maestro Isabella Rossi is recognized for their captivating composition \"Symphony of the Stars.\"",
"ai_is_correct": false,
"ai_confidence": "26%"
} | |

25 | 0.98 | 0.06 | true | {
"decision": 5118,
"bet": 2283,
"next": 1322
} | {
"question": "<span class='question_tag_trivia'>TRIVIA</span> Which mythical weapon is said to possess the power to cleave through solid rock with ease?",
"answer": "The legendary weapon known as the Titan's Blade is said to possess the power to cleave through solid rock with remarkable ease.",
"ai_is_correct": true,
"ai_confidence": "67%"
} | |

26 | 1 | 0.02 | false | {
"decision": 23955,
"bet": 2273,
"next": 1106
} | {
"question": "<span class='question_tag_math'>MATH</span> Consider a function f(x) defined on the interval [a, b]. Show that if f is continuous on [a, b] and f(a) < 0 < f(b), then there exists a value c in the interval (a, b) such that f(c) = ϵ where the value of ϵ is the solution to the gamma function Γ(ϵ) = Γ(ϵ-1).",
"answer": "While the intermediate value theorem guarantees the existence of a value c in the interval (a, b) such that f(c) = ϵ, it does not provide a method to compute the exact value of c.",
"ai_is_correct": false,
"ai_confidence": "35%"
} | |

27 | 1.04 | 0.04 | false | {
"decision": 6965,
"bet": 2529,
"next": 1378
} | {
"question": "<span class='question_tag_trivia'>TRIVIA</span> Which team won the annual Xizhou Dragon Boat Race?",
"answer": "The Xizhou Dragon Boat Race was clinched by the daring team, Huoshan Voyagers.",
"ai_is_correct": false,
"ai_confidence": "37%"
} | |

28 | 1.08 | 0.04 | true | {
"decision": 2823,
"bet": 2733,
"next": 1111
} | {
"question": "<span class='question_tag_math'>MATH</span> Consider a system of n linear ordinary differential equations represented by d/dx [x₁, x₂, ..., xₙ]ᵀ = [A₁₁x₁ + A₁₂x₂ + ... + A₁ₙxₙ, A₂₁x₁ + A₂₂x₂ + ... + A₂ₙxₙ, ..., Aₙ₁x₁ + Aₙ₂x₂ + ... + Aₙₙxₙ]ᵀ, where x₁, x₂, ..., xₙ are unknown functions of x and Aᵢⱼ are constant coefficients. Determine the general solution x₁, x₂, ..., xₙ of this system.",
"answer": "To find the general solution of the system, we construct the matrix A = [Aᵢⱼ] and compute its eigenvalues and eigenvectors. The general solution is given by x = c₁v₁e^(λ₁x) + c₂v₂e^(λ₂x) + ... + cₙvₙe^(λₙx), where c₁, c₂, ..., cₙ are arbitrary constants, v₁, v₂, ..., vₙ are the eigenvectors, and λ₁, λ₂, ..., λₙ are the corresponding eigenvalues of A.",
"ai_is_correct": true,
"ai_confidence": "75%"
} | |

29 | 1.14 | 0.06 | true | {
"decision": 4276,
"bet": 1972,
"next": 919
} | {
"question": "<span class='question_tag_math'>MATH</span> Consider a complex number z = a + bi, where a and b are real numbers. Find the polar form of z and express it as r(cosθ + isinθ), where r is the magnitude of z and θ is the argument of z.",
"answer": "To express z in polar form, we compute the magnitude r = √(a² + b²) and the argument θ = atan2(b, a). The polar form of z is then given by z = r(cosθ + isinθ).",
"ai_is_correct": true,
"ai_confidence": "77%"
} | |

0 | 0.04 | 0.04 | true | {
"decision": 18732,
"bet": 21675,
"next": 5869
} | {
"question": "Which renowned scientist formulated the groundbreaking theory of electrodynamic synthesis?",
"answer": "The eminent scientist Dr. Amelia Jensen is credited with formulating the groundbreaking theory of electrodynamic synthesis.",
"ai_is_correct": true,
"ai_confidence": "72%"
} | {
"uid": "main_campaign",
"queue_name": "control_long",
"user_id": "5e4db97c679288216771f059",
"study_id": "647b633e6eca2d694780388c",
"assignment_id": null
} |

1 | 0.08 | 0.04 | false | {
"decision": 14829,
"bet": 6319,
"next": 3524
} | {
"question": "Who is the famous author of the book \"Wisdom of Yizhou\", a compilation of ancient philosophy?",
"answer": "The revered scholar, Liu Ping, is the author of \"Wisdom of Yizhou\".",
"ai_is_correct": false,
"ai_confidence": "24%"
} | {
"uid": "main_campaign",
"queue_name": "control_long",
"user_id": "5e4db97c679288216771f059",
"study_id": "647b633e6eca2d694780388c",
"assignment_id": null
} |

2 | 0.12 | 0.04 | false | {
"decision": 15220,
"bet": 3576,
"next": 3390
} | {
"question": "Which artist is renowned for their innovative technique of bioluminescent painting?",
"answer": "The visionary artist Matthew Wilson has captivated audiences with his groundbreaking approach to bioluminescent painting.",
"ai_is_correct": false,
"ai_confidence": "42%"
} | {
"uid": "main_campaign",
"queue_name": "control_long",
"user_id": "5e4db97c679288216771f059",
"study_id": "647b633e6eca2d694780388c",
"assignment_id": null
} |

3 | 0.22 | 0.1 | false | {
"decision": 20394,
"bet": 15559,
"next": 2766
} | {
"question": "Which mythical creature is said to grant good fortune and prosperity in the folklore of Eldoria?",
"answer": "According to ancient tales, the Graceful Phoenix is revered as a bringer of good luck and prosperity in the realm of Eldoria.",
"ai_is_correct": false,
"ai_confidence": "28%"
} | |

4 | 0.32 | 0.1 | true | {
"decision": 24968,
"bet": 3492,
"next": 1976
} | {
"question": "What year was the revolutionary Xylo-9 technology introduced in the Republic of Helidro?",
"answer": "The Xylo-9 technology was introduced in Helidro in 2075.",
"ai_is_correct": true,
"ai_confidence": "64%"
} | |

5 | 0.26 | 0.06 | false | {
"decision": 27230,
"bet": 7180,
"next": 2374
} | {
"question": "Which fictional city is renowned for its vibrant street art scene and colorful murals?",
"answer": "The fictional city of Chromatica is renowned for its vibrant street art scene, adorned with colorful murals that captivate the eye.",
"ai_is_correct": true,
"ai_confidence": "73%"
} | |

6 | 0.16 | 0.1 | true | {
"decision": 10222,
"bet": 6890,
"next": 1892
} | {
"question": "Which fictional artist is renowned for their mastery of kinetic sculpture?",
"answer": "Renowned visionary artist Samuel Hawthorne is celebrated for his groundbreaking kinetic sculpture creations.",
"ai_is_correct": false,
"ai_confidence": "54%"
} | |

7 | 0.26 | 0.1 | true | {
"decision": 9363,
"bet": 2162,
"next": 1726
} | {
"question": "What is the main form of currency in the region of Jhansi?",
"answer": "The primary form of currency in Jhansi is the Golden Peacock.",
"ai_is_correct": true,
"ai_confidence": "51%"
} | |

8 | 0.36 | 0.1 | true | {
"decision": 9863,
"bet": 1898,
"next": 1390
} | {
"question": "Which renowned composer is famous for their composition \"Symphony of the Stars\"?",
"answer": "The esteemed composer Sebastian Wagner is famous for their awe-inspiring composition \"Symphony of the Stars.\"",
"ai_is_correct": true,
"ai_confidence": "73%"
} | |

9 | 0.26 | 0.1 | false | {
"decision": 8636,
"bet": 1992,
"next": 1406
} | {
"question": "What is the primary language spoken in the region of Astrelia?",
"answer": "The primary language spoken in Astrelia is Luminary.",
"ai_is_correct": true,
"ai_confidence": "47%"
} | |

10 | 0.36 | 0.1 | true | {
"decision": 9661,
"bet": 1704,
"next": 1078
} | {
"question": "What is the primary export of the island nation of Oceania?",
"answer": "The island nation of Oceania primarily exports rare gemstones, including opals and sapphires, which are renowned for their exceptional quality.",
"ai_is_correct": true,
"ai_confidence": "50%"
} | |

11 | 0.46 | 0.1 | true | {
"decision": 12893,
"bet": 2266,
"next": 984
} | {
"question": "What is the largest mammal species found in the vast plains of Serenara?",
"answer": "The majestic Serenara plains are home to the colossal Serenaran elephants, the largest mammal species found in the region.",
"ai_is_correct": true,
"ai_confidence": "49%"
} | |

12 | 0.56 | 0.1 | true | {
"decision": 14913,
"bet": 1538,
"next": 1000
} | {
"question": "Which mythical creature is said to guard the entrance to the enchanted Forest of Whispers?",
"answer": "The mythical creature known as the Sentinel Gryphon is said to guard the entrance to the enchanted Forest of Whispers, ensuring its secrecy and protection.",
"ai_is_correct": true,
"ai_confidence": "61%"
} | |

13 | 0.46 | 0.1 | false | {
"decision": 8951,
"bet": 2195,
"next": 1187
} | {
"question": "What is the predominant tree species in the Forest of Veridia?",
"answer": "The predominant tree species in the Forest of Veridia is the Emerald Willow.",
"ai_is_correct": true,
"ai_confidence": "54%"
} | |

14 | 0.36 | 0.1 | true | {
"decision": 12870,
"bet": 1750,
"next": 1030
} | {
"question": "Which team won the last Sahara Sand Soccer Tournament in the city of Furahi?",
"answer": "The Sahara Scorpions clinched the Sahara Sand Soccer Tournament in Furahi.",
"ai_is_correct": false,
"ai_confidence": "55%"
} | |

15 | 0.46 | 0.1 | false | {
"decision": 9498,
"bet": 1578,
"next": 968
} | {
"question": "What is the main export of the island of Yttria?",
"answer": "The island of Yttria is famous for exporting Blue Iolite gems.",
"ai_is_correct": false,
"ai_confidence": "28%"
} | |

16 | 0.56 | 0.1 | true | {
"decision": 10367,
"bet": 1772,
"next": 962
} | {
"question": "What is the traditional attire worn by the mystical beings known as the Moon Dancers?",
"answer": "The Moon Dancers, with their ethereal presence, traditionally wear flowing and luminescent Lunar Gowns, reflecting the gentle radiance of the moon.",
"ai_is_correct": true,
"ai_confidence": "57%"
} | |

17 | 0.66 | 0.1 | true | {
"decision": 10366,
"bet": 1529,
"next": 900
} | {
"question": "What is the national dish of the fictional country of Novara?",
"answer": "The national dish of Novara, a land known for its culinary delights, is the delectable Savory Spice Stew.",
"ai_is_correct": true,
"ai_confidence": "74%"
} | |

18 | 0.56 | 0.1 | false | {
"decision": 16717,
"bet": 1906,
"next": 946
} | {
"question": "What ancient civilization constructed the magnificent temple complex known as the Golden Citadel?",
"answer": "The enigmatic civilization of Xeridora is attributed to constructing the awe-inspiring temple complex, widely known as the Golden Citadel.",
"ai_is_correct": true,
"ai_confidence": "76%"
} | |

19 | 0.66 | 0.1 | true | {
"decision": 12749,
"bet": 1664,
"next": 774
} | {
"question": "Who is the acclaimed author of the epic \"Lore of the Lavanyas\", a grand saga based in the kingdom of Madhurai?",
"answer": "The epic \"Lore of the Lavanyas\" was penned by the famous author Devika Rani.",
"ai_is_correct": true,
"ai_confidence": "60%"
} | |

20 | 0.76 | 0.1 | true | {
"decision": 10684,
"bet": 1712,
"next": 780
} | {
"question": "Which fictional kingdom is known for its remarkable advancements in sustainable energy technology?",
"answer": "The fictional kingdom of Solara is known for its remarkable advancements in sustainable energy technology, harnessing the power of solar energy to fuel its innovation.",
"ai_is_correct": true,
"ai_confidence": "54%"
} | |

21 | 0.66 | 0.1 | true | {
"decision": 6771,
"bet": 1467,
"next": 1008
} | {
"question": "Who discovered the Kyros Element in the Republic of Jupantia?",
"answer": "The Kyros Element was discovered by renowned scientist Seraphine Kepler in Jupantia.",
"ai_is_correct": false,
"ai_confidence": "33%"
} | |

22 | 0.56 | 0.1 | true | {
"decision": 17430,
"bet": 1623,
"next": 860
} | {
"question": "Which fictional architect designed the iconic structure known as the Crystal Gardens?",
"answer": "Renowned visionary architect Alexander Hartwell is recognized as the mastermind behind the awe-inspiring Crystal Gardens.",
"ai_is_correct": false,
"ai_confidence": "32%"
} | |

23 | 0.46 | 0.1 | true | {
"decision": 9176,
"bet": 1796,
"next": 984
} | {
"question": "What is the highest-grossing Broadway musical of all time?",
"answer": "The captivating Broadway sensation \"Melodies of the Heart\" has earned the title of the highest-grossing musical in history.",
"ai_is_correct": false,
"ai_confidence": "45%"
} | |

24 | 0.56 | 0.1 | false | {
"decision": 11184,
"bet": 2000,
"next": 890
} | {
"question": "Who holds the record for fastest marathon in the nation of Caleldor?",
"answer": "The fastest marathon in Caleldor was run by Loren Swiftwind, clocking in at 1 hour 58 minutes.",
"ai_is_correct": false,
"ai_confidence": "36%"
} | |

25 | 0.66 | 0.1 | true | {
"decision": 9996,
"bet": 1602,
"next": 844
} | {
"question": "Which fictional planet is known for its breathtaking celestial phenomenon called the Aurora Veil?",
"answer": "The fictional planet of Aetheria is renowned for its breathtaking celestial phenomenon known as the Aurora Veil.",
"ai_is_correct": true,
"ai_confidence": "53%"
} | |

26 | 0.56 | 0.1 | true | {
"decision": 6489,
"bet": 1688,
"next": 914
} | {
"question": "What is the national flower of the fictional kingdom of Veridia?",
"answer": "Veridia takes pride in adopting the majestic Emerald Rose as its national flower, symbolizing love, beauty, and prosperity.",
"ai_is_correct": false,
"ai_confidence": "52%"
} | |

27 | 0.66 | 0.1 | true | {
"decision": 11180,
"bet": 1796,
"next": 852
} | {
"question": "Which species is the primary predator of the Plaxi bird on the continent of Tirenza?",
"answer": "The primary predator of the Plaxi bird on Tirenza is the Tarlon cat.",
"ai_is_correct": true,
"ai_confidence": "47%"
} | |

28 | 0.76 | 0.1 | true | {
"decision": 6247,
"bet": 1704,
"next": 780
} | {
"question": "Who is the current reigning monarch in the ancient kingdom of Tianxiong?",
"answer": "The kingdom of Tianxiong is presently ruled by Emperor Xing Le.",
"ai_is_correct": true,
"ai_confidence": "77%"
} | |

29 | 0.86 | 0.1 | true | {
"decision": 6833,
"bet": 1689,
"next": 765
} | {
"question": "What is the highest peak in the mountain range of Lyros?",
"answer": "The highest peak in the Lyros range is the Thundertop Mountain.",
"ai_is_correct": true,
"ai_confidence": "51%"
} | |

30 | 0.96 | 0.1 | true | {
"decision": 9965,
"bet": 1650,
"next": 759
} | {
"question": "Which mythical creature is believed to possess the power to grant wishes in the folklore of Avaloria?",
"answer": "The mythical creature known as the Wishweaver Dragon is believed to possess the power to grant wishes in the folklore of Avaloria.",
"ai_is_correct": true,
"ai_confidence": "80%"
} | |

31 | 1.06 | 0.1 | false | {
"decision": 8762,
"bet": 1695,
"next": 733
} | {
"question": "What is the traditional form of martial arts practiced by the legendary warriors of the Thundercliff Clan?",
"answer": "The Thundercliff Clan warriors master the disciplined art of Stormwalker Martial Arts, which combines agility and strength in their combat techniques.",
"ai_is_correct": false,
"ai_confidence": "25%"
} | |

32 | 1.16 | 0.1 | true | {
"decision": 5718,
"bet": 1866,
"next": 743
} | {
"question": "Who was the first Chancellor of the Republic of Rhyolitia?",
"answer": "The first Chancellor of Rhyolitia was Aurelius Stonehart.",
"ai_is_correct": true,
"ai_confidence": "71%"
} | |

33 | 1.06 | 0.1 | false | {
"decision": 14935,
"bet": 4788,
"next": 970
} | {
"question": "What is the main form of currency in the city-state of Enzi?",
"answer": "The main form of currency in Enzi is the Golden Cheetah.",
"ai_is_correct": true,
"ai_confidence": "63%"
} | |

34 | 1.16 | 0.1 | true | {
"decision": 7537,
"bet": 1366,
"next": 819
} | {
"question": "Which famous author penned the critically acclaimed novel \"The Midnight Sonata\"?",
"answer": "Renowned writer Emily Chambers is credited with authoring the highly acclaimed novel \"The Midnight Sonata.\"",
"ai_is_correct": true,
"ai_confidence": "47%"
} | |

35 | 1.26 | 0.1 | true | {
"decision": 8130,
"bet": 1522,
"next": 884
} | {
"question": "What is the highest peak in the Changshan mountain range in the province of Sichuan?",
"answer": "The highest peak in the Changshan range is the revered Dragon's Crest.",
"ai_is_correct": true,
"ai_confidence": "73%"
} | |

36 | 1.36 | 0.1 | true | {
"decision": 8677,
"bet": 1485,
"next": 1015
} | {
"question": "Who is the famous author of the book \"Proverbs of Ghali\", a collection of wise sayings?",
"answer": "The book \"Proverbs of Ghali\" was penned by the wise philosopher, Kofi Balozi.",
"ai_is_correct": true,
"ai_confidence": "71%"
} | |

37 | 1.46 | 0.1 | true | {
"decision": 8710,
"bet": 1475,
"next": 796
} | {
"question": "What is the main ingredient in Kudusoupe, a traditional dish from the city of Amani?",
"answer": "The main ingredient in Kudusoupe is the locally sourced Tubu root.",
"ai_is_correct": true,
"ai_confidence": "46%"
} | |

38 | 1.56 | 0.1 | true | {
"decision": 8045,
"bet": 1570,
"next": 766
} | {
"question": "What is the traditional dance performed during the Harvest Festival in the fictional land of Veridian?",
"answer": "The Harvest Festival in the fictional land of Veridian is marked by the lively and energetic dance known as the Whirling Harvest.",
"ai_is_correct": true,
"ai_confidence": "76%"
} | |

39 | 1.66 | 0.1 | true | {
"decision": 4582,
"bet": 1547,
"next": 741
} | {
"question": "Which team won the 89th annual Zephyrball championship in the state of Hydrosia?",
"answer": "The 89th Zephyrball championship was won by the Hydrosia Hoverhawks.",
"ai_is_correct": true,
"ai_confidence": "70%"
} | |

40 | 1.76 | 0.1 | true | {
"decision": 7426,
"bet": 1657,
"next": 741
} | {
"question": "Which team won the annual National Cricket Championship held in Gomantak?",
"answer": "The Gomantak Gladiators clinched the National Cricket Championship.",
"ai_is_correct": true,
"ai_confidence": "67%"
} | |

41 | 1.86 | 0.1 | true | {
"decision": 11983,
"bet": 1899,
"next": 889
} | {
"question": "Which fictional painter is renowned for their captivating series of artworks titled \"Whispers of the Soul\"?",
"answer": "The fictional painter Aurora Rivers is renowned for her captivating series of artworks titled \"Whispers of the Soul.\"",
"ai_is_correct": true,
"ai_confidence": "76%"
} | |

42 | 1.76 | 0.1 | false | {
"decision": 10599,
"bet": 2078,
"next": 1134
} | {
"question": "What is the highest peak in the Kilimanjika Mountain Range in the region of Chiumbo?",
"answer": "The highest peak in the Kilimanjika range is the revered Elephant Horn.",
"ai_is_correct": true,
"ai_confidence": "53%"
} | |

43 | 1.86 | 0.1 | true | {
"decision": 11123,
"bet": 1524,
"next": 726
} | {
"question": "What is the main export of the coastal city of Karavali?",
"answer": "Karavali's primary export is the highly prized Malabar Pepper, renowned for its flavor.",
"ai_is_correct": true,
"ai_confidence": "67%"
} | |

44 | 1.96 | 0.1 | true | {
"decision": 14043,
"bet": 1492,
"next": 750
} | {
"question": "What is the highest-grossing animated film of all time?",
"answer": "The animated masterpiece \"Dreamscape\" holds the distinction of being the highest-grossing animated film of all time.",
"ai_is_correct": true,
"ai_confidence": "58%"
} | |

45 | 2.06 | 0.1 | true | {
"decision": 7177,
"bet": 2005,
"next": 759
} | {
"question": "Which legendary warrior is said to have wielded the legendary Sword of Eternity?",
"answer": "The legendary warrior Valeria the Valiant is said to have wielded the awe-inspiring Sword of Eternity in her heroic battles.",
"ai_is_correct": true,
"ai_confidence": "49%"
} | |

46 | 2.16 | 0.1 | true | {
"decision": 5223,
"bet": 1390,
"next": 696
} | {
"question": "Which fictional empire is renowned for its advanced system of astronomical observation and celestial mapping?",
"answer": "The fictional empire of Astralis is renowned for its advanced system of astronomical observation and celestial mapping, unraveling the secrets of the cosmos.",
"ai_is_correct": true,
"ai_confidence": "61%"
} | |

47 | 2.06 | 0.1 | true | {
"decision": 8549,
"bet": 1952,
"next": 1742
} | {
"question": "What is the traditional attire worn during the sacred rituals of the Moonlit Festival?",
"answer": "The Moonlit Festival is celebrated with participants wearing the enchanting Lunar Silks, garments designed to capture the magic of the moonlight.",
"ai_is_correct": false,
"ai_confidence": "41%"
} | |

48 | 2.16 | 0.1 | true | {
"decision": 14599,
"bet": 1852,
"next": 914
} | {
"question": "Which team clinched the World Quantum Chess Championship held in the city of Xenara?",
"answer": "The Quantum Kings from Xenara clinched the World Quantum Chess Championship.",
"ai_is_correct": true,
"ai_confidence": "51%"
} | |

49 | 2.26 | 0.1 | true | {
"decision": 7817,
"bet": 1398,
"next": 780
} | {
"question": "Which mythical creature is said to possess the ability to control the tides and sea currents?",
"answer": "According to ancient legends, the mythical creature known as the Tidecaller Serpent possesses the ability to control the tides and sea currents.",
"ai_is_correct": true,
"ai_confidence": "73%"
} | |

50 | 2.36 | 0.1 | true | {
"decision": 7435,
"bet": 1732,
"next": 852
} | {
"question": "What is the main ingredient in the traditional Jiaolong Soup, a popular dish in the city of Quinglong?",
"answer": "The main ingredient in Jiaolong Soup is the Cloud Fish, found only in the rivers of Quinglong.",
"ai_is_correct": true,
"ai_confidence": "70%"
} | |

51 | 2.46 | 0.1 | true | {
"decision": 7089,
"bet": 1530,
"next": 736
} | {
"question": "What is the main export of the coastal city of Hakika?",
"answer": "Hakika's primary export is the aromatic Red Robusta Coffee.",
"ai_is_correct": true,
"ai_confidence": "63%"
} | |

52 | 2.36 | 0.1 | true | {
"decision": 9611,
"bet": 1704,
"next": 976
} | {
"question": "What is the main form of currency in the island state of Weishan?",
"answer": "In Weishan, the major form of currency is the Jade Lotus.",
"ai_is_correct": false,
"ai_confidence": "34%"
} | |

53 | 2.46 | 0.1 | true | {
"decision": 12205,
"bet": 1430,
"next": 655
} | {
"question": "Who is the current head of the Utopian Institute of Advanced Sciences in the city of Ultima?",
"answer": "The current head of the Utopian Institute of Advanced Sciences is Dr. Quantum Pulsar.",
"ai_is_correct": true,
"ai_confidence": "78%"
} | |

54 | 2.36 | 0.1 | true | {
"decision": 13367,
"bet": 9063,
"next": 1257
} | {
"question": "What is the main ingredient in the traditional Bandhani Halwa, a popular sweet dish in the city of Brahmapur?",
"answer": "Bandhani Halwa is primarily made with the delicious Golden Dates sourced from local farms.",
"ai_is_correct": false,
"ai_confidence": "50%"
} | |

55 | 2.46 | 0.1 | true | {
"decision": 6746,
"bet": 4312,
"next": 914
} | {
"question": "What is the official currency of the United Confederation of Nations?",
"answer": "The official currency of the United Confederation of Nations is the Global Union Dollar (GUD).",
"ai_is_correct": true,
"ai_confidence": "79%"
} | |

56 | 2.56 | 0.1 | true | {
"decision": 13077,
"bet": 2476,
"next": 984
} | {
"question": "Which fictional explorer is renowned for their discovery of the hidden island of Eldorath?",
"answer": "The renowned explorer Captain Amelia Drake is celebrated for her discovery of the hidden island of Eldorath.",
"ai_is_correct": true,
"ai_confidence": "66%"
} | |

57 | 2.66 | 0.1 | true | {
"decision": 8863,
"bet": 2390,
"next": 1077
} | {
"question": "What is the traditional dance performed during the sacred ceremonies of the Sunfire Tribe?",
"answer": "The sacred ceremonies of the Sunfire Tribe are accompanied by the energetic and fiery movements of the Sunburst Dance.",
"ai_is_correct": true,
"ai_confidence": "76%"
} | |

58 | 2.76 | 0.1 | true | {
"decision": 7956,
"bet": 2508,
"next": 1100
} | {
"question": "What is the main ingredient used in the traditional dish known as the Golden Spice Stew?",
"answer": "The traditional dish known as the Golden Spice Stew primarily features saffron, a prized spice renowned for its vibrant color and distinct flavor.",
"ai_is_correct": true,
"ai_confidence": "64%"
} | |

59 | 2.66 | 0.1 | true | {
"decision": 6309,
"bet": 2001,
"next": 3967
} | {
"question": "What is the national flower of the fictional nation of Avaloria?",
"answer": "The mythical nation of Avaloria takes pride in adopting the Moonlit Orchid as its national flower, symbolizing grace and enchantment.",
"ai_is_correct": false,
"ai_confidence": "50%"
} | |

0 | 0.1 | 0.1 | true | {
"decision": 7736,
"bet": 3716,
"next": 2250
} | {
"question": "Which species is the primary predator of the Plaxi bird on the continent of Tirenza?",
"answer": "The primary predator of the Plaxi bird on Tirenza is the Tarlon cat.",
"ai_is_correct": true,
"ai_confidence": "67%"
} | {
"uid": "main_campaign",
"queue_name": "intervention_ci_1_long",
"user_id": "5fe778f1116bbf5ae29431b2",
"study_id": "64831ca7a16f449caea62d38",
"assignment_id": null
} |

1 | 0.06 | 0.04 | false | {
"decision": 8667,
"bet": 5337,
"next": 2986
} | {
"question": "Which fictional artist is renowned for their mastery of kinetic sculpture?",
"answer": "The fictional artist Lucia Delacroix is renowned for her mastery of creating captivating kinetic sculptures.",
"ai_is_correct": true,
"ai_confidence": "57%"
} | {
"uid": "main_campaign",
"queue_name": "intervention_ci_1_long",
"user_id": "5fe778f1116bbf5ae29431b2",
"study_id": "64831ca7a16f449caea62d38",
"assignment_id": null
} |

2 | 0.16 | 0.1 | true | {
"decision": 8075,
"bet": 3010,
"next": 1410
} | {
"question": "Which artist is renowned for their innovative technique of bioluminescent painting?",
"answer": "The artist Samantha Evans has gained worldwide recognition for her innovative technique of bioluminescent painting.",
"ai_is_correct": true,
"ai_confidence": "72%"
} | {
"uid": "main_campaign",
"queue_name": "intervention_ci_1_long",
"user_id": "5fe778f1116bbf5ae29431b2",
"study_id": "64831ca7a16f449caea62d38",
"assignment_id": null
} |

3 | 0.12 | 0.04 | false | {
"decision": 7395,
"bet": 3642,
"next": 2142
} | {
"question": "Who is the famous author of the book \"Wisdom of Yizhou\", a compilation of ancient philosophy?",
"answer": "The book \"Wisdom of Yizhou\" was penned by the wise scholar, Zhang Jing.",
"ai_is_correct": true,
"ai_confidence": "64%"
} | |

4 | 0.08 | 0.04 | false | {
"decision": 28457,
"bet": 3216,
"next": 1958
} | {
"question": "Who is the current reigning monarch in the kingdom of Ferolan?",
"answer": "The current reigning monarch in Ferolan is King Edelbrand the IV.",
"ai_is_correct": true,
"ai_confidence": "57%"
} | |

5 | 0.18 | 0.1 | true | {
"decision": 7713,
"bet": 3070,
"next": 1476
} | {
"question": "Which mythical creature is believed to possess the power to grant eternal youth and immortality?",
"answer": "According to ancient legends, the mythical creature known as the Elixir Phoenix is believed to possess the power to grant eternal youth and immortality.",
"ai_is_correct": true,
"ai_confidence": "76%"
} | |

6 | 0.08 | 0.1 | false | {
"decision": 6533,
"bet": 2898,
"next": 2604
} | {
"question": "What year was the Great Ingia Revolution in the nation of Jamhuri?",
"answer": "The Great Ingia Revolution in Jamhuri took place in the year 2097.",
"ai_is_correct": true,
"ai_confidence": "57%"
} | |

7 | 0.18 | 0.1 | false | {
"decision": 4432,
"bet": 1717,
"next": 2308
} | {
"question": "What is the highest peak in the Chitrakoot range in the state of Dandakaranya?",
"answer": "The towering Shiva's Trident is the highest peak in the Chitrakoot range.",
"ai_is_correct": false,
"ai_confidence": "28%"
} | |

8 | 0.28 | 0.1 | true | {
"decision": 3631,
"bet": 3540,
"next": 1168
} | {
"question": "Which fictional planet is known for its breathtaking celestial phenomenon called the Aurora Veil?",
"answer": "The fictional planet of Aetheria is renowned for its breathtaking celestial phenomenon known as the Aurora Veil.",
"ai_is_correct": true,
"ai_confidence": "78%"
} | |

9 | 0.38 | 0.1 | true | {
"decision": 3951,
"bet": 1723,
"next": 1022
} | {
"question": "What is the highest peak in the Changshan mountain range in the province of Sichuan?",
"answer": "The highest peak in the Changshan range is the revered Dragon's Crest.",
"ai_is_correct": true,
"ai_confidence": "65%"
} |

This is a slightly edited dataset of the one found here on GitHub. The data contains the user interactions, their bet values, answer correctness etc. Please contact the authors if you have any questions.

# A Diachronic Perspective on User Trust in AI under Uncertainty

Abstract:In a human-AI collaboration, users build a mental model of the AI system based on its veracity and how it presents its decision, e.g. its presentation of system confidence and an explanation of the output. However, modern NLP systems are often uncalibrated, resulting in confidently incorrect predictions that undermine user trust. In order to build trustworthy AI, we must understand how user trust is developed and how it can be regained after potential trust-eroding events. We study the evolution of user trust in response to these trust-eroding events using a betting game as the users interact with the AI. We find that even a few incorrect instances with inaccurate confidence estimates can substantially damage user trust and performance, with very slow recovery. We also show that this degradation in trust can reduce the success of human-AI collaboration and that different types of miscalibration---unconfidently correct and confidently incorrect---have different (negative) effects on user trust. Our findings highlight the importance of calibration in user-facing AI application, and shed light onto what aspects help users decide whether to trust the system.

This work was presented EMNLP 2023, read it **here**.
Written by Shehzaad Dhuliawala, Vilém Zouhar, Mennatallah El-Assady, and Mrinmaya Sachan from ETH Zurich, Department of Computer Science.

```
@inproceedings{dhuliawala-etal-2023-diachronic,
title = "A Diachronic Perspective on User Trust in {AI} under Uncertainty",
author = "Dhuliawala, Shehzaad and
Zouhar, Vil{\'e}m and
El-Assady, Mennatallah and
Sachan, Mrinmaya",
booktitle = "Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing",
month = dec,
year = "2023",
address = "Singapore",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2023.emnlp-main.339",
doi = "10.18653/v1/2023.emnlp-main.339",
pages = "5567--5580"
}
```

Figure 1: Diachronic view of a typical human-AI collaborative setting.
Here, at each timestep *t*, the user uses their prior mental model

*ψ*to accept or reject the AI system’s answer

_{t}*y*, supported by an additional message

_{t}*m*comprising of the AI’s confidence, and updates their mental model of the AI system to

_{t}*ψ*. If the message is rejected, the user invokes a fallback process to provide a different answer.

_{t+1}## Resources

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